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Elapsed time problems

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5159473
Tim spends \(20\) minutes on math homework and then \(25\) minutes on language arts homework. How many minutes does Tim spend on homework altogether?

Hints

- What two time intervals are given? - Should you add or subtract to find the total time?

Solution

1. Add the two time intervals: \(20\,\text{min} + 25\,\text{min} = 45\,\text{min}\).

Answer

Tim spends \(45\) minutes on homework altogether.
5206343
A small apple tree was planted in a garden in 2012. On the same date in 2024, the family checks how long it has been there. How many full years have passed?

Hints

- Count forward from the earlier year to the later year. - Which operation finds the difference between two years? - Find the difference between \(2024\) and \(2012\).

Solution

1. Subtract the planting year from the later year: \(2024 - 2012 = 12\). 2. Therefore, \(12\) full years have passed.

Answer

\(12\) full years have passed.
5212523
How many days are there altogether in January, February, and March? Assume February has \(28\) days.

Hints

- Write the number of days in each month. - February has \(28\) days in this problem. - Add the three numbers.

Solution

1. January has \(31\) days, February has \(28\) days, and March has \(31\) days. 2. Add the days: \(31 + 28 + 31 = 90\).

Answer

The first three months have \(90\) days altogether.
5212793
Find how many hours after noon each time occurs. a) \(5{:}00\) p.m. b) \(8{:}00\) p.m. c) \(10{:}00\) p.m. d) Midnight

Hints

- Start counting at noon. - Each hour on the clock is one more hour after noon. - Midnight is half a day after noon.

Solution

1. Count forward from noon to each time. 2. Noon to \(5{:}00\) p.m. is \(5\) hours. 3. Noon to \(8{:}00\) p.m. is \(8\) hours. 4. Noon to \(10{:}00\) p.m. is \(10\) hours. 5. Noon to midnight is \(12\) hours.

Answer

a) \(5\) hours b) \(8\) hours c) \(10\) hours d) \(12\) hours
5165183
The table shows bus departure times and travel times. Find the arrival time for each route. <table> <tr><th>Bus route</th><th>Departure</th><th>Travel time</th></tr> <tr><td>Route A</td><td>\(9{:}10\) a.m.</td><td>\(50\,\text{min}\)</td></tr> <tr><td>Route B</td><td>\(11{:}30\) a.m.</td><td>\(1\,\text{hr}\ 15\,\text{min}\)</td></tr> <tr><td>Route C</td><td>\(3{:}45\) p.m.</td><td>\(40\,\text{min}\)</td></tr> </table>

Hints

- Add each travel time to its departure time. - One hour equals \(60\) minutes. - For Route C, count to the next hour first.

Solution

1. Route A arrives at \(10{:}00\) a.m. because \(9{:}10\) a.m. plus \(50\) minutes is \(10{:}00\) a.m. 2. Route B arrives at \(12{:}45\) p.m. because \(11{:}30\) a.m. plus \(1\) hour \(15\) minutes is \(12{:}45\) p.m. 3. Route C arrives at \(4{:}25\) p.m. Count \(15\) minutes to \(4{:}00\) p.m., then add the remaining \(25\) minutes.

Answer

Route A: \(10{:}00\) a.m. Route B: \(12{:}45\) p.m. Route C: \(4{:}25\) p.m.
5177773
An analog wall clock shows the numbers \(1\) through \(12\). During one full day, the hour hand travels around the clock face twice. a) How many hours pass during one full trip around the clock face? b) How many hours are in a full day? c) It is exactly \(7{:}00\) a.m. What time will it be after one full trip of the hour hand?

Hints

- How many numbered hour positions are on the clock face? - How many times does the hour hand pass \(12\) before the clock shows the same hour in the evening? - What happens when you add exactly \(12\) hours to a time?

Solution

1. One full trip of the hour hand around a clock numbered \(1\) through \(12\) represents \(12\) hours. 2. Two full trips represent \(12 \times 2 = 24\) hours. 3. Add \(12\) hours to \(7{:}00\) a.m. The time will be \(7{:}00\) p.m.

Answer

a) \(12\) hours b) \(24\) hours c) \(7{:}00\) p.m.
5201143
Mrs. Meyer takes a train trip. The outbound ride lasts \(2\) hours \(15\) minutes, and the return ride lasts \(1\) hour \(35\) minutes. How long does she spend on the train altogether?

Hints

- Decide whether the two travel times should be added or subtracted. - Add the hours, then add the minutes. - Check whether the minutes make another full hour.

Solution

1. Add the hours: \(2\,\text{hr} + 1\,\text{hr} = 3\,\text{hr}\). 2. Add the minutes: \(15\,\text{min} + 35\,\text{min} = 50\,\text{min}\). 3. The total is \(3\) hours \(50\) minutes.

Answer

Mrs. Meyer spends \(3\) hours \(50\) minutes on the train.
5201363
Mrs. Miller begins work at \(8{:}15\) a.m. She works for \(4\) hours \(30\) minutes. At what time does her workday end?

Hints

- Are you looking for the starting time or the ending time? - Add the full hours first. - Then add the remaining minutes.

Solution

1. Add \(4\) hours to \(8{:}15\) a.m. to get \(12{:}15\) p.m. 2. Add \(30\) minutes to get \(12{:}45\) p.m.

Answer

Her workday ends at \(12{:}45\) p.m.
5212473
It is \(4{:}00\) p.m. How many hours are left until midnight?

Hints

- Count forward from \(4{:}00\) p.m. to midnight. - You can split the time into two easier intervals. - Add the lengths of the intervals.

Solution

1. From \(4{:}00\) p.m. to \(8{:}00\) p.m. is \(4\) hours. 2. From \(8{:}00\) p.m. to midnight is another \(4\) hours. 3. Add the intervals: \(4 + 4 = 8\) hours.

Answer

There are \(8\) hours left until midnight.
5313603
Continue the time pattern shown on clocks 1 through 3. How much time passes between consecutive clocks? Give the times for the next two clocks.
Figure for problem 531360

Hints

- Find the elapsed time from clock 1 to clock 2. - Check whether the same interval leads to clock 3. - Keep adding that interval.

Solution

1. The clocks show \(8{:}00\), \(8{:}30\), and \(9{:}00\). 2. Each time is \(30\) minutes after the previous time. 3. Add \(30\) minutes to \(9{:}00\) to get \(9{:}30\). 4. Add another \(30\) minutes to get \(10{:}00\).

Answer

The interval is \(30\) minutes. The next two times are \(9{:}30\) and \(10{:}00\).
5313753
How much time passes between the two clocks? Both times are in the morning on the same day.
Figure for problem 531375

Hints

- Read the time on clock a). - Read the time on clock b). - Find the difference in minutes.

Solution

1. Clock a) shows \(8{:}00\) a.m. 2. Clock b) shows \(8{:}45\) a.m. 3. The elapsed time is \(45\) minutes.

Answer

\(45\) minutes pass.
5314183
Mia starts her homework in the afternoon at the time shown on clock a) and finishes at the time shown on clock b). How many minutes does she spend on her homework?
Figure for problem 531418

Hints

- Read the starting and ending times. - Both times are within the same hour. - Find the difference between the minute values.

Solution

1. Clock a) shows \(2{:}15\) p.m. 2. Clock b) shows \(2{:}45\) p.m. 3. Subtract the minute values: \(45 - 15 = 30\).

Answer

Mia spends \(30\) minutes on her homework.
5314193
A cake must bake for exactly \(45\) minutes. The clock shows the afternoon time when the cake is put in the oven. What time should the cake be taken out?
Figure for problem 531419

Hints

- Read the starting time carefully. - Add the baking time to the starting time. - Track where the minute hand moves after \(45\) minutes.

Solution

1. The clock shows \(3{:}10\) p.m. 2. Add \(45\) minutes: \(10 + 45 = 55\) minutes. 3. The cake should be taken out at \(3{:}55\) p.m.

Answer

The cake should be taken out at \(3{:}55\) p.m.
5314213
The clock shows a time shortly before noon. How many minutes are left until \(12{:}00\) noon?
Figure for problem 531421

Hints

- Read the minutes carefully. - How many minutes are in a full hour? - Find the difference between \(42\) minutes and \(60\) minutes.

Solution

1. The clock shows \(11{:}42\) a.m. 2. Subtract from a full hour: \(60 - 42 = 18\) minutes.

Answer

There are \(18\) minutes left until noon.
5314223
Paul has two clocks in his room. Clock A shows the correct time. Clock B is \(5\) minutes fast. What time does clock B show when clock A shows the time in the picture?
Figure for problem 531422

Hints

- A fast clock shows a later time than the correct time. - Decide whether to add or subtract the \(5\) minutes.

Solution

1. Clock A shows \(8{:}35\). 2. A clock that is \(5\) minutes fast shows a time \(5\) minutes later. 3. Add \(5\) minutes: \(8{:}35 + 5\) minutes is \(8{:}40\).

Answer

Clock B shows \(8{:}40\).
5314233
Find the elapsed time between clocks 1 and 2.
Figure for problem 531423

Hints

- Read both clock times. - The hour is the same, so find the difference between the minutes.

Solution

1. Clock 1 shows \(6{:}15\). 2. Clock 2 shows \(6{:}55\). 3. Since the hour stays the same, subtract the minutes: \(55 - 15 = 40\).

Answer

The elapsed time is \(40\) minutes.
5383653
A workshop meets Monday from \(3{:}00\) p.m. to \(4{:}00\) p.m., Tuesday from \(2{:}30\) p.m. to \(3{:}30\) p.m., and Thursday from \(3{:}15\) p.m. to \(4{:}15\) p.m. a) How long is each meeting? b) How many hours of workshop time are scheduled altogether?

Hints

- Compare each start and end time. - Add the three meeting lengths.

Solution

1. Each ending time is \(1\) hour after its starting time. 2. There are three \(1\)-hour meetings, so the total is \(3\) hours.

Answer

a) Each meeting lasts \(1\) hour. b) \(3\) hours
5100113
Louis set his alarm for \(7{:}35\) a.m. When he woke up, it was \(6{:}23\) a.m. How many minutes were left until the alarm would ring?

Hints

- Picture a clock and count forward from the wake-up time to the alarm time. - It may help to count to the next hour first. - Then count the remaining minutes to the alarm time. - Do not treat hours and minutes like decimal numbers.

Solution

1. From \(6{:}23\) a.m. to \(7{:}23\) a.m. is \(60\) minutes. 2. From \(7{:}23\) a.m. to \(7{:}35\) a.m. is another \(12\) minutes. 3. Add the intervals: \(60 + 12 = 72\) minutes.

Answer

\(72\,\text{min}\)
5100203
Leo is attending a summer math camp. The first class begins at \(9{:}45\,\text{a.m.}\). Each class period lasts \(45\) minutes, and there is a \(10\)-minute break between class periods. Lunch begins right after the fourth class period. What time does lunch begin?

Hints

- How many minutes of class are there altogether? - How many breaks occur between the first and fourth class periods? - Add the class time and break time, then add that duration to the starting time.

Solution

1. Find the total class time: \(4 \times 45\,\text{minutes} = 180\,\text{minutes} = 3\,\text{hours}\). 2. There are \(3\) breaks between \(4\) class periods, so the total break time is \(3 \times 10\,\text{minutes} = 30\,\text{minutes}\). 3. Add the class time and break time: \(3\,\text{hours} + 30\,\text{minutes} = 3\,\text{hours}\,30\,\text{minutes}\). 4. Add the total elapsed time to the starting time: \(9{:}45\,\text{a.m.} + 3\,\text{hours}\,30\,\text{minutes} = 1{:}15\,\text{p.m.}\).

Answer

Lunch begins at \(1{:}15\,\text{p.m.}\).
5159413
Paul starts a mountain hike at \(10{:}15\) a.m. He hikes uphill for \(45\) minutes to an overlook, rests there for \(20\) minutes, and then hikes another \(50\) minutes to the summit. At what time does Paul reach the summit?

Hints

- First find when Paul reaches the overlook. - Add the rest time next. - After the rest, count to the next hour and then add the remaining minutes. - Work through the time intervals one at a time.

Solution

1. Find the arrival time at the overlook: \(10{:}15\) a.m. plus \(45\) minutes is \(11{:}00\) a.m. 2. Add the rest time: \(11{:}00\) a.m. plus \(20\) minutes is \(11{:}20\) a.m. 3. Add the final hiking time: \(11{:}20\) a.m. plus \(50\) minutes is \(12{:}10\) p.m.

Answer

Paul reaches the summit at \(12{:}10\) p.m.
5159423
Lucas begins making a cake at \(2{:}40\) p.m. Mixing the ingredients takes \(15\) minutes. Then the batter rests for \(45\) minutes. Finally, the cake bakes for \(35\) minutes. At what time can Lucas take the finished cake out of the oven?

Hints

- Identify the starting time. - Find the time after each stage: mixing, resting, and baking. - Remember that \(60\) minutes make \(1\) hour.

Solution

1. Find when mixing ends: \(2{:}40\) p.m. plus \(15\) minutes is \(2{:}55\) p.m. 2. Add the resting time: \(2{:}55\) p.m. plus \(45\) minutes is \(3{:}40\) p.m. 3. Add the baking time: \(3{:}40\) p.m. plus \(35\) minutes is \(4{:}15\) p.m.

Answer

Lucas can take the cake out of the oven at \(4{:}15\) p.m.
5159433
Emma and Jonah meet at the library at \(1{:}30\) p.m. to work on a report. They spend \(1\) hour \(15\) minutes finding information, take a \(25\)-minute break, and then spend \(55\) minutes writing. At what time do they finish their work?

Hints

- Start with the meeting time and add each time interval in order. - When crossing an hour, count to the next hour first. - Keep hours and minutes separate as you calculate.

Solution

1. Find when the research ends: \(1{:}30\) p.m. plus \(1\) hour \(15\) minutes is \(2{:}45\) p.m. 2. Add the break: \(2{:}45\) p.m. plus \(25\) minutes is \(3{:}10\) p.m. 3. Add the writing time: \(3{:}10\) p.m. plus \(55\) minutes is \(4{:}05\) p.m.

Answer

They finish at \(4{:}05\) p.m.
5159483
The Miller family leaves home for a movie at \(4{:}10\) p.m. The movie begins at \(4{:}35\) p.m. and lasts exactly \(90\) minutes. a) How many minutes pass between leaving home and the start of the movie? b) How many minutes pass altogether between leaving home and the end of the movie?

Hints

- First find the time from leaving home until the movie begins. - Add the time before the movie to the movie's length. - Check whether the answer should be in minutes or hours.

Solution

1. From \(4{:}10\) p.m. to \(4{:}35\) p.m. is \(25\) minutes. 2. Add the movie's length: \(25\,\text{min} + 90\,\text{min} = 115\,\text{min}\).

Answer

a) \(25\) minutes b) \(115\) minutes
5159493
Jonah begins a hike to a mountain lodge at \(9{:}45\) a.m. He hikes for \(50\) minutes, takes a \(15\)-minute break, and then hikes another \(30\) minutes to reach the lodge. a) How much time passes from the start of the hike until Jonah reaches the lodge? b) At what time does Jonah reach the lodge?

Hints

- Add all the hiking and break times first. - How many minutes are in \(1\) hour? - Add the total duration to the start time in steps.

Solution

1. Add the time intervals: \(50\,\text{min} + 15\,\text{min} + 30\,\text{min} = 95\,\text{min}\). 2. Convert the duration: \(95\,\text{min} = 1\) hour \(35\) minutes. 3. Add the duration to the start time: \(9{:}45\) a.m. plus \(1\) hour is \(10{:}45\) a.m., and another \(35\) minutes gives \(11{:}20\) a.m.

Answer

a) \(95\) minutes, or \(1\) hour \(35\) minutes b) \(11{:}20\) a.m.
5160923
A soccer game, including halftime, lasts exactly \(105\) minutes. The game ends at \(5{:}20\,\text{p.m.}\). What time did the game begin?

Hints

- First rewrite the total duration in hours and minutes. - Work backward from the ending time. - Subtract the hour first, then subtract the remaining minutes.

Solution

1. Rewrite the duration in hours and minutes: \(105\,\text{minutes} = 1\,\text{hour}\,45\,\text{minutes}\). 2. Subtract \(1\) hour from the ending time: \(5{:}20\,\text{p.m.} - 1\,\text{hour} = 4{:}20\,\text{p.m.}\). 3. Subtract the remaining \(45\) minutes: \(4{:}20\,\text{p.m.} - 45\,\text{minutes} = 3{:}35\,\text{p.m.}\).

Answer

The game began at \(3{:}35\,\text{p.m.}\).
5161093
An overnight train leaves a station at \(9{:}15\,\text{p.m.}\) and arrives at its destination at \(6{:}45\,\text{a.m.}\) the next morning. How long is the train trip?

Hints

- Find the elapsed time from the departure time to midnight. - Find the elapsed time from midnight to the arrival time. - Add the two time intervals. - Regroup if the minutes total more than \(60\).

Solution

1. Find the time from departure to midnight: From \(9{:}15\,\text{p.m.}\) to \(12{:}00\,\text{a.m.}\) is \(2\,\text{hours}\,45\,\text{minutes}\). 2. Find the time from midnight to arrival: From \(12{:}00\,\text{a.m.}\) to \(6{:}45\,\text{a.m.}\) is \(6\,\text{hours}\,45\,\text{minutes}\). 3. Add the two time intervals: \(2\,\text{hours}\,45\,\text{minutes} + 6\,\text{hours}\,45\,\text{minutes} = 8\,\text{hours}\,90\,\text{minutes}\). 4. Regroup \(90\) minutes as \(1\) hour \(30\) minutes. The total is \(9\,\text{hours}\,30\,\text{minutes}\).

Answer

The train trip lasts \(9\,\text{hours}\,30\,\text{minutes}\).
5161113
A guided overnight hike begins at \(10{:}50\,\text{p.m.}\). The group returns to the starting point at \(3{:}15\,\text{a.m.}\) the next morning. How long does the hike last?

Hints

- Find the time before midnight and the time after midnight separately. - How many minutes are there from \(10{:}50\,\text{p.m.}\) to \(11{:}00\,\text{p.m.}\)? - Add the hours and minutes from the two intervals.

Solution

1. Find the time from the start to midnight: From \(10{:}50\,\text{p.m.}\) to \(11{:}00\,\text{p.m.}\) is \(10\) minutes, and from \(11{:}00\,\text{p.m.}\) to \(12{:}00\,\text{a.m.}\) is \(1\) hour. That is \(1\,\text{hour}\,10\,\text{minutes}\). 2. Find the time after midnight: From \(12{:}00\,\text{a.m.}\) to \(3{:}15\,\text{a.m.}\) is \(3\,\text{hours}\,15\,\text{minutes}\). 3. Add the two time intervals: \(1\,\text{hour}\,10\,\text{minutes} + 3\,\text{hours}\,15\,\text{minutes} = 4\,\text{hours}\,25\,\text{minutes}\).

Answer

The hike lasts \(4\,\text{hours}\,25\,\text{minutes}\).
5162773
A summer camp runs from July 18 through August 3. How many days does the camp last? Count both the first day and the last day.

Hints

- How many days are in July? - Count the days from the starting date through the end of July, including July 18. - Add the days in August.

Solution

1. July has \(31\) days. From July 18 through July 31, there are \(31 - 18 + 1 = 14\) days. 2. From August 1 through August 3, there are \(3\) more days. 3. Add the days from the two months: \(14 + 3 = 17\) days.

Answer

The camp lasts \(17\) days.
5162793
Lara says, “My trip from February 25 through March 10 lasts exactly \(14\) days.” The year is not a leap year. Use a calculation to decide whether Lara is correct.

Hints

- How many days are in February during a non-leap year? - Count the trip days in February, including February 25. - Add the trip days in March. - Compare your result with Lara’s claim.

Solution

1. In a non-leap year, February has \(28\) days. From February 25 through February 28, there are \(28 - 25 + 1 = 4\) days. 2. From March 1 through March 10, there are \(10\) days. 3. Add the two parts: \(4 + 10 = 14\) days. 4. The calculated duration matches Lara’s claim.

Answer

Yes. Lara is correct because the trip lasts exactly \(14\) days.
5164933
Lucas takes a train to visit his grandparents. The train leaves at \(2{:}25\) p.m. and arrives at \(4{:}10\) p.m. How long is the train ride?

Hints

- First find the number of minutes to the next hour. - Then count from that hour to the arrival time. - You can calculate the hours and minutes separately.

Solution

1. From \(2{:}25\) p.m. to \(3{:}00\) p.m. is \(35\) minutes. 2. From \(3{:}00\) p.m. to \(4{:}10\) p.m. is \(1\) hour \(10\) minutes. 3. Add the intervals: \(35\) minutes plus \(1\) hour \(10\) minutes equals \(1\) hour \(45\) minutes.

Answer

The train ride lasts \(1\) hour \(45\) minutes.
5164943
Two buses travel from Chicago to Milwaukee. Bus A leaves at \(9{:}10\) a.m. and arrives at \(10{:}45\) a.m. Bus B leaves at \(11{:}45\) a.m. and arrives at \(1{:}15\) p.m. Which bus takes less time? What is the difference in minutes?

Hints

- Find each bus's travel time separately. - Compare the two travel times. - “Less time” means the shorter duration.

Solution

1. Bus A travels from \(9{:}10\) a.m. to \(10{:}45\) a.m., which is \(1\) hour \(35\) minutes. 2. Bus B travels from \(11{:}45\) a.m. to \(1{:}15\) p.m., which is \(1\) hour \(30\) minutes. 3. Bus B takes less time because \(1\) hour \(30\) minutes is less than \(1\) hour \(35\) minutes. 4. The difference is \(5\) minutes.

Answer

Bus B takes less time. The difference is \(5\) minutes.
5164953
A ferry takes visitors to an island. The schedule shows three trips: <table> <tr> <td><strong>Trip</strong></td> <td><strong>Departure</strong></td> <td><strong>Arrival</strong></td> </tr> <tr> <td>Trip 1</td> <td>\(8{:}20\) a.m.</td> <td>\(9{:}05\) a.m.</td> </tr> <tr> <td>Trip 2</td> <td>\(10{:}45\) a.m.</td> <td>\(11{:}40\) a.m.</td> </tr> <tr> <td>Trip 3</td> <td>\(1{:}15\) p.m.</td> <td>\(2{:}05\) p.m.</td> </tr> </table> Find the duration of each trip. Which trip lasts the longest?

Hints

- Make a list of the duration of each trip. - Count forward from each departure time to its arrival time. - Compare all three durations.

Solution

1. Trip 1 lasts from \(8{:}20\) a.m. to \(9{:}05\) a.m., which is \(45\) minutes. 2. Trip 2 lasts from \(10{:}45\) a.m. to \(11{:}40\) a.m., which is \(55\) minutes. 3. Trip 3 lasts from \(1{:}15\) p.m. to \(2{:}05\) p.m., which is \(50\) minutes. 4. Since \(45 < 50 < 55\), Trip 2 lasts the longest.

Answer

Trip 1 lasts \(45\) minutes, Trip 2 lasts \(55\) minutes, and Trip 3 lasts \(50\) minutes. Trip 2 lasts the longest.
5165053
A family is planning a train trip from Boston to Providence. The schedule shows departure and arrival times. <table> <thead> <tr><th>Train</th><th>Departure from Boston</th><th>Arrival in Providence</th></tr> </thead> <tbody> <tr><td>Train A</td><td>\(9{:}15\) a.m.</td><td>\(10{:}25\) a.m.</td></tr> <tr><td>Train B</td><td>\(10{:}15\) a.m.</td><td>\(11{:}40\) a.m.</td></tr> <tr><td>Train C</td><td>\(11{:}15\) a.m.</td><td>\(12{:}25\) p.m.</td></tr> </tbody> </table> 1) How many minutes longer is the trip on Train B than the trip on Train A? 2) How long is the trip on Train C, in hours and minutes?

Hints

- Find the travel time for each train. - Count to the next hour, then add the remaining minutes. - Subtract the two travel times for part 1).

Solution

1. Train A takes \(1\) hour \(10\) minutes, or \(70\) minutes. 2. Train B takes \(1\) hour \(25\) minutes, or \(85\) minutes. 3. The difference is \(85 - 70 = 15\) minutes. 4. Train C takes \(1\) hour \(10\) minutes.

Answer

1) Train B takes \(15\) minutes longer. 2) Train C takes \(1\) hour \(10\) minutes.
5165323
Lucas has two activities on Tuesday afternoon. Find each activity's duration, then compare them. <table> <tr> <td>Activity</td> <td>Start</td> <td>End</td> </tr> <tr> <td>Soccer practice</td> <td>\(4{:}15\) p.m.</td> <td>\(5{:}45\) p.m.</td> </tr> <tr> <td>Guitar lesson</td> <td>\(3{:}30\) p.m.</td> <td>\(4{:}15\) p.m.</td> </tr> </table> Which activity lasts longer? How many minutes longer is it?

Hints

- How many minutes are in a full hour? - Count from each start time to its end time in steps. - Subtract the shorter duration from the longer duration.

Solution

1. Soccer practice lasts from \(4{:}15\) p.m. to \(5{:}45\) p.m., which is \(90\) minutes. 2. The guitar lesson lasts from \(3{:}30\) p.m. to \(4{:}15\) p.m., which is \(45\) minutes. 3. Find the difference: \(90\,\text{min} - 45\,\text{min} = 45\,\text{min}\).

Answer

Soccer practice lasts \(90\) minutes, and the guitar lesson lasts \(45\) minutes. Soccer practice is \(45\) minutes longer.
5165333
Two buses travel from downtown to the zoo. The table shows their departure and arrival times. <table> <tr> <td>Bus</td> <td>Departure</td> <td>Arrival</td> </tr> <tr> <td>Route A</td> <td>\(9{:}15\) a.m.</td> <td>\(10{:}48\) a.m.</td> </tr> <tr> <td>Route B</td> <td>\(11{:}30\) a.m.</td> <td>\(1{:}05\) p.m.</td> </tr> </table> Find each travel time in minutes. Which bus takes more time?

Hints

- First count any full hours that pass. - Then add the remaining minutes to the arrival time. - Remember that \(1\) hour is \(60\) minutes.

Solution

1. Route A takes \(60\) minutes from \(9{:}15\) a.m. to \(10{:}15\) a.m. and \(33\) more minutes to \(10{:}48\) a.m., for \(93\) minutes total. 2. Route B takes \(60\) minutes from \(11{:}30\) a.m. to \(12{:}30\) p.m., then \(30\) minutes to \(1{:}00\) p.m., and \(5\) more minutes to \(1{:}05\) p.m., for \(95\) minutes total. 3. Since \(95 > 93\), Route B takes more time.

Answer

Route A takes \(93\) minutes, and Route B takes \(95\) minutes. Route B takes more time.
5165343
Three children's programs air on Saturday afternoon. <table> <tr> <td>Program</td> <td>Start</td> <td>End</td> </tr> <tr> <td>Science</td> <td>\(2{:}15\) p.m.</td> <td>\(2{:}50\) p.m.</td> </tr> <tr> <td>Nature</td> <td>\(3{:}05\) p.m.</td> <td>\(3{:}45\) p.m.</td> </tr> <tr> <td>Sports</td> <td>\(4{:}20\) p.m.</td> <td>\(4{:}55\) p.m.</td> </tr> </table> Find the duration of each program in minutes. Which program is the longest?

Hints

- When the hour stays the same, subtract the starting minutes from the ending minutes. - Record the duration of each program separately. - Compare all three durations.

Solution

1. Science lasts \(50 - 15 = 35\) minutes. 2. Nature lasts \(45 - 5 = 40\) minutes. 3. Sports lasts \(55 - 20 = 35\) minutes. 4. Nature is the longest program at \(40\) minutes.

Answer

Science lasts \(35\) minutes, Nature lasts \(40\) minutes, and Sports lasts \(35\) minutes. Nature is the longest.
5166133
A school fair begins at \(10{:}20\,\text{a.m.}\) and ends at \(4{:}15\,\text{p.m.}\). Admission costs \(\$2.50\) for adults and \(\$1.00\) for children. During the fair, the concession stand sells \(120\) hot dogs. How many hours and minutes pass from the beginning to the end of the school fair?

Hints

- Which information in the problem is actually needed to find the elapsed time? - Count forward to the next hour first. - How many full hours pass after that? - Add the minutes from the beginning and end of the interval.

Solution

1. Find the time from \(10{:}20\,\text{a.m.}\) to \(11{:}00\,\text{a.m.}\): \(40\) minutes. 2. Find the time from \(11{:}00\,\text{a.m.}\) to \(4{:}00\,\text{p.m.}\): \(5\) hours. 3. Find the time from \(4{:}00\,\text{p.m.}\) to \(4{:}15\,\text{p.m.}\): \(15\) minutes. 4. Add the intervals: \(5\,\text{hours} + 40\,\text{minutes} + 15\,\text{minutes} = 5\,\text{hours}\,55\,\text{minutes}\).

Answer

The school fair lasts \(5\,\text{hours}\,55\,\text{minutes}\).
5169133
A movie begins at \(4{:}10\,\text{p.m.}\). Sarah wants to arrive \(20\) minutes early to meet her friends. It takes her \(15\) minutes to walk from home to the theater. What is the latest time Sarah can leave home?

Hints

- First find the time Sarah wants to arrive at the theater. - Then work backward by the length of the walk. - Count backward in minutes one step at a time.

Solution

1. Find the time Sarah wants to arrive: \(4{:}10\,\text{p.m.} - 20\,\text{minutes} = 3{:}50\,\text{p.m.}\). 2. Subtract the walking time: \(3{:}50\,\text{p.m.} - 15\,\text{minutes} = 3{:}35\,\text{p.m.}\).

Answer

Sarah must leave home by \(3{:}35\,\text{p.m.}\).
5169153
The Miller family wants to arrive at their grandparents’ home by \(11{:}30\,\text{a.m.}\) on Sunday. The drive takes \(1\) hour \(20\) minutes, and loading the car takes \(15\) minutes. What is the latest time the family can begin loading the car?

Hints

- First work backward to find the latest time the car can leave. - Remember to include the time needed to load the car. - Work backward in two steps.

Solution

1. Find the latest departure time: \(11{:}30\,\text{a.m.} - 1\,\text{hour}\,20\,\text{minutes} = 10{:}10\,\text{a.m.}\). 2. Subtract the loading time: \(10{:}10\,\text{a.m.} - 15\,\text{minutes} = 9{:}55\,\text{a.m.}\).

Answer

The family must begin loading the car by \(9{:}55\,\text{a.m.}\).
5171683
Use the schedule for a sightseeing boat: <table> <tr> <td>Harbor Point</td> <td>departs</td> <td>\(9{:}20\,\text{a.m.}\)</td> </tr> <tr> <td>Bay Village</td> <td>arrives</td> <td>\(9{:}55\,\text{a.m.}\)</td> </tr> <tr> <td>Bay Village</td> <td>departs</td> <td>\(10{:}05\,\text{a.m.}\)</td> </tr> <tr> <td>Lighthouse Pier</td> <td>arrives</td> <td>\(11{:}15\,\text{a.m.}\)</td> </tr> </table> a) How many minutes does the boat spend traveling from Harbor Point to Bay Village? b) How much time passes from the departure at Harbor Point to the arrival at Lighthouse Pier? Give the answer in hours and minutes.

Hints

- Count the minutes from one time to the next. - For the full trip, count from the first departure to the final arrival. - The words “departs” and “arrives” tell you which times begin and end each interval.

Solution

1. Find the first travel time: From \(9{:}20\,\text{a.m.}\) to \(9{:}55\,\text{a.m.}\) is \(35\) minutes. 2. Find the full elapsed time: From \(9{:}20\,\text{a.m.}\) to \(11{:}20\,\text{a.m.}\) would be \(2\) hours. The boat arrives \(5\) minutes earlier, so the elapsed time is \(1\) hour \(55\) minutes.

Answer

a) The first boat ride takes \(35\) minutes. b) The total elapsed time is \(1\) hour \(55\) minutes.
5171783
Migrating birds return in the spring. The table shows when storks arrive in two cities: <table> <tr> <th>City</th> <th>Arrival date</th> </tr> <tr> <td>Oakville</td> <td>March 28</td> </tr> <tr> <td>Lake City</td> <td>April 11</td> </tr> </table> How many weeks later do the storks arrive in Lake City than in Oakville?

Hints

- How many days are in March? - Count the days remaining in March, then add the days in April. - Divide the total number of days by the number of days in one week.

Solution

1. March has \(31\) days. From March 28 to March 31 is \(31 - 28 = 3\) days. 2. From March 31 to April 11 is another \(11\) days. 3. Add the days: \(3 + 11 = 14\) days. 4. Convert days to weeks: \(14 \div 7 = 2\) weeks.

Answer

The storks arrive \(2\) weeks later in Lake City.
5171893
A bakery accepts advance orders for special items. The table shows how many days each item takes to prepare: <table> <tr> <th>Item</th> <th>Preparation time</th> </tr> <tr> <td>Fruit tart</td> <td>\(2\) days</td> </tr> <tr> <td>Gift basket</td> <td>\(5\) days</td> </tr> <tr> <td>Wedding cake</td> <td>\(10\) days</td> </tr> <tr> <td>Chocolate assortment</td> <td>\(4\) days</td> </tr> </table> Ms. Smith orders all four items on April 26. On what date will each item be ready for pickup? April has \(30\) days.

Hints

- How many days are in April? - Add each preparation time to April 26. - When a result is greater than \(30\), continue counting into May. - May comes after April.

Solution

1. Fruit tart: \(26 + 2 = 28\), so it is ready on April 28. 2. Gift basket: \(26 + 5 = 31\). Since April has \(30\) days, it is ready on May 1. 3. Wedding cake: \(26 + 10 = 36\). Subtract the \(30\) days in April: \(36 - 30 = 6\), so it is ready on May 6. 4. Chocolate assortment: \(26 + 4 = 30\), so it is ready on April 30.

Answer

Fruit tart: April 28 Gift basket: May 1 Wedding cake: May 6 Chocolate assortment: April 30
5177733
The longest day of the year in a certain city has \(16\) hours of daylight. How many hours does the shortest night have? If the sun rises at \(5{:}00\) a.m. that day, at what time does it set?

Hints

- How many hours are in a full day and night? - Subtract the daylight hours to find the hours of darkness. - Count forward \(16\) hours from \(5{:}00\) a.m.

Solution

1. A full day has \(24\) hours, so the night lasts \(24\,\text{hr} - 16\,\text{hr} = 8\,\text{hr}\). 2. Add \(16\) hours to the sunrise time: \(5{:}00\) a.m. plus \(16\) hours is \(9{:}00\) p.m.

Answer

The night lasts \(8\) hours, and the sun sets at \(9{:}00\) p.m.
5177743
In a far northern location, the longest summer day has \(19\) hours of daylight. A winter day there has \(14\) fewer hours of daylight than the summer day. How many hours of daylight are there on a winter day? How many hours does the night last on that winter day?

Hints

- First use the difference from summer to find the winter daylight time. - A full day has \(24\) hours. - Subtract the daylight hours from \(24\) to find the nighttime hours.

Solution

1. Find the winter daylight time: \(19\,\text{hr} - 14\,\text{hr} = 5\,\text{hr}\). 2. Subtract the daylight time from a full day: \(24\,\text{hr} - 5\,\text{hr} = 19\,\text{hr}\).

Answer

A winter day has \(5\) hours of daylight, and the night lasts \(19\) hours.
5177753
Mrs. Meyer works each day from \(8{:}00\) a.m. to \(12{:}00\) p.m. and again from \(2{:}00\) p.m. to \(5{:}00\) p.m. How many hours of the \(24\)-hour day is she not at work?

Hints

- How many hours are in a full day? - First find how many hours she works altogether. - Find the length of each work interval.

Solution

1. The first work period lasts \(12 - 8 = 4\) hours. 2. The second work period lasts \(5 - 2 = 3\) hours. 3. Mrs. Meyer works \(4 + 3 = 7\) hours altogether. 4. Subtract from the full day: \(24 - 7 = 17\) hours.

Answer

Mrs. Meyer is not at work for \(17\) hours of the day.
5177763
Lucas says, “I sleep from \(9{:}00\) p.m. to \(7{:}00\) a.m. That is almost half a day!” A full day has \(24\) hours. How many hours does Lucas actually sleep? How many more hours would he need to sleep for exactly half a day?

Hints

- How many hours are in half of a day? - Split the sleep time into the hours before midnight and the hours after midnight. - Subtract to find the difference between the two durations.

Solution

1. From \(9{:}00\) p.m. to midnight is \(3\) hours. 2. From midnight to \(7{:}00\) a.m. is \(7\) hours. 3. Lucas sleeps \(3 + 7 = 10\) hours. 4. Half a day is \(24 \div 2 = 12\) hours. 5. The difference is \(12 - 10 = 2\) hours.

Answer

Lucas sleeps \(10\) hours. He would need \(2\) more hours to sleep for half a day.
5177783
A woodworking shop has two work periods. The first begins at \(7{:}30\) a.m. and ends at \(12{:}00\) p.m. After lunch, the second begins at \(1{:}00\) p.m. and ends at \(4{:}30\) p.m. a) How long is the first work period? b) How long is the lunch break? c) How many hours of work are completed altogether?

Hints

- Find the time from the start to the end of the first work period. - The break is the interval between the two work periods. - Add the two work durations, remembering that \(60\) minutes make \(1\) hour.

Solution

1. The first work period from \(7{:}30\) a.m. to \(12{:}00\) p.m. lasts \(4\) hours \(30\) minutes. 2. The lunch break from \(12{:}00\) p.m. to \(1{:}00\) p.m. lasts \(1\) hour. 3. The second work period from \(1{:}00\) p.m. to \(4{:}30\) p.m. lasts \(3\) hours \(30\) minutes. 4. Add the work periods: \(4\) hours \(30\) minutes plus \(3\) hours \(30\) minutes equals \(8\) hours.

Answer

a) \(4\) hours \(30\) minutes b) \(1\) hour c) \(8\) hours
5181703
A regional train leaves the station at \(9{:}25\,\text{a.m.}\). The trip lasts \(4\) hours \(50\) minutes. What time does the train arrive?

Hints

- Add the full hours first. - Then add the remaining minutes. - Regroup when the minutes pass the next hour.

Solution

1. Add the hours: \(9{:}25\,\text{a.m.} + 4\,\text{hours} = 1{:}25\,\text{p.m.}\). 2. Add the minutes: \(1{:}25\,\text{p.m.} + 50\,\text{minutes} = 2{:}15\,\text{p.m.}\).

Answer

The train arrives at \(2{:}15\,\text{p.m.}\).
5181713
An author event at the public library begins at \(3{:}40\,\text{p.m.}\). The author reads for \(45\) minutes, there is a \(15\)-minute break, and then she answers questions for \(25\) minutes. What time does the event end?

Hints

- Add the lengths of all parts of the event. - Convert the total minutes to hours and minutes. - Add that duration to the starting time.

Solution

1. Find the total length of the event: \(45 + 15 + 25 = 85\) minutes. 2. Rewrite the duration: \(85\) minutes is \(1\) hour \(25\) minutes. 3. Add the duration to the starting time: \(3{:}40\,\text{p.m.} + 1\,\text{hour}\,25\,\text{minutes} = 5{:}05\,\text{p.m.}\).

Answer

The event ends at \(5{:}05\,\text{p.m.}\).
5181763
A bus stop lists these departure times: Line A: \(7{:}45\) a.m. Line B: \(1{:}20\) p.m. Line C: \(8{:}05\) p.m. a) How much time passes from Line A's departure to Line B's departure? b) How much time passes from Line B's departure to Line C's departure? c) How much time passes from Line A's departure to Line C's departure?

Hints

- Break an interval at noon when that makes the calculation easier. - Count the full hours first, then the remaining minutes. - The total interval from Line A to Line C equals the sum of the first two intervals.

Solution

1. a) From \(7{:}45\) a.m. to \(12{:}00\) p.m. is \(4\) hours \(15\) minutes, and from \(12{:}00\) p.m. to \(1{:}20\) p.m. is \(1\) hour \(20\) minutes. The total is \(5\) hours \(35\) minutes. 2. b) From \(1{:}20\) p.m. to \(8{:}05\) p.m. is \(6\) hours \(45\) minutes. 3. c) Add the two intervals: \(5\,\text{hr}\ 35\,\text{min}+6\,\text{hr}\ 45\,\text{min}=12\,\text{hr}\ 20\,\text{min}\).

Answer

a) \(5\,\text{hr}\ 35\,\text{min}\) b) \(6\,\text{hr}\ 45\,\text{min}\) c) \(12\,\text{hr}\ 20\,\text{min}\)
5181773
Lucas looks at a digital clock. It is \(5{:}15\,\text{p.m.}\). a) What time will it be \(45\) minutes later? b) Lucas says, “I started my homework exactly \(3\) hours ago.” What time did he start? c) How much time passes from \(5{:}15\,\text{p.m.}\) to \(8{:}30\,\text{p.m.}\)?

Hints

- For part a), count forward to the next hour. - For part b), subtract the full hours from the given time. - For part c), count the full hours first, then the remaining minutes.

Solution

1. Add \(45\) minutes to \(5{:}15\,\text{p.m.}\): \(5{:}15\,\text{p.m.} + 45\,\text{minutes} = 6{:}00\,\text{p.m.}\). 2. Subtract \(3\) hours from \(5{:}15\,\text{p.m.}\): \(5{:}15\,\text{p.m.} - 3\,\text{hours} = 2{:}15\,\text{p.m.}\). 3. From \(5{:}15\,\text{p.m.}\) to \(8{:}15\,\text{p.m.}\) is \(3\) hours, and the remaining time to \(8{:}30\,\text{p.m.}\) is \(15\) minutes. The elapsed time is \(3\) hours \(15\) minutes.

Answer

a) \(6{:}00\,\text{p.m.}\) b) \(2{:}15\,\text{p.m.}\) c) \(3\) hours \(15\) minutes
5181823
A class begins a nature field trip at \(8{:}35\,\text{a.m.}\) and returns to school at \(12{:}10\,\text{p.m.}\). How much time passes?

Hints

- Count from the starting time to the next full hour. - Count the full hours between the two times. - Add the minutes at the beginning and end of the interval. - A time line may help you organize the parts.

Solution

1. From \(8{:}35\,\text{a.m.}\) to \(9{:}00\,\text{a.m.}\) is \(25\) minutes. 2. From \(9{:}00\,\text{a.m.}\) to \(12{:}00\,\text{p.m.}\) is \(3\) hours. 3. From \(12{:}00\,\text{p.m.}\) to \(12{:}10\,\text{p.m.}\) is \(10\) minutes. 4. Add the intervals: \(3\,\text{hours} + 25\,\text{minutes} + 10\,\text{minutes} = 3\,\text{hours}\,35\,\text{minutes}\).

Answer

The field trip lasts \(3\) hours \(35\) minutes.
5181873
Swimming Class A begins at \(2{:}20\,\text{p.m.}\) and ends at \(3{:}50\,\text{p.m.}\). Swimming Class B lasts exactly \(100\) minutes. Which class is longer, and by how many minutes?

Hints

- First find the elapsed time for Class A. - Convert Class A’s time to minutes. - Compare the two durations. - Subtract to find the difference.

Solution

1. Find the length of Class A: From \(2{:}20\,\text{p.m.}\) to \(3{:}50\,\text{p.m.}\) is \(1\) hour \(30\) minutes. 2. Convert Class A’s length to minutes: \(60 + 30 = 90\) minutes. 3. Compare the classes: Class B lasts \(100\) minutes, while Class A lasts \(90\) minutes. 4. Find the difference: \(100 - 90 = 10\) minutes.

Answer

Class B is longer by \(10\) minutes.
5182123
A hiking group starts at \(10{:}15\,\text{a.m.}\) and reaches its destination at \(2{:}30\,\text{p.m.}\). The group takes a \(45\)-minute lunch break. How long does the group actually spend walking?

Hints

- First find the total time from the start to the finish. - Then subtract the break time. - Regroup one hour as \(60\) minutes if needed.

Solution

1. Find the full elapsed time: From \(10{:}15\,\text{a.m.}\) to \(2{:}30\,\text{p.m.}\) is \(4\) hours \(15\) minutes. 2. Subtract the lunch break: \(4\,\text{hours}\,15\,\text{minutes} - 45\,\text{minutes} = 3\,\text{hours}\,30\,\text{minutes}\).

Answer

The group spends \(3\) hours \(30\) minutes walking.
5190663
A gardener plants a flower seed on May 25. The seed sprouts exactly \(10\) days later. On what date will it sprout?

Hints

- How many days are in May? - How many days are there after May 25 through the end of May? - Count the remaining days into the next month.

Solution

1. There are \(31 - 25 = 6\) days after May 25 in May. 2. After those \(6\) days, \(10 - 6 = 4\) more days remain. 3. Count the remaining \(4\) days into June. The seed sprouts on June 4.

Answer

The seed will sprout on June 4.
5190673
Two classes conduct science experiments. Class 3A starts an experiment on June 22, and it ends exactly \(12\) days later. Class 3B starts an experiment on June 26, and it ends exactly \(8\) days later. Find the ending date for each experiment. What do you notice?

Hints

- How many days are in June? - Find each ending date separately. - Continue counting into July when you pass June 30. - Compare the two ending dates.

Solution

1. Count \(12\) days after June 22. Since June has \(30\) days, the ending date is July 4. 2. Count \(8\) days after June 26. The ending date is also July 4. 3. Both experiments end on the same date.

Answer

Both experiments end on July 4. They have different starting dates and durations but the same ending date.
5190813
Leo plants sunflower seeds on March 15. The directions say the first flowers will bloom exactly \(65\) days later. On what date will the sunflowers bloom?

Hints

- How many days are in March and April? - Find how many days remain in March after March 15. - Count forward one month at a time. - A list of the months and their lengths may help.

Solution

1. March has \(31\) days, so there are \(31 - 15 = 16\) days after March 15 in March. 2. Subtract those days: \(65 - 16 = 49\) days remain. 3. April has \(30\) days, so \(49 - 30 = 19\) days remain. 4. Count \(19\) days into May. The sunflowers bloom on May 19.

Answer

The sunflowers will bloom on May 19.
5190823
Two children begin reading projects on May 25. Lucas plans to finish his book exactly \(50\) days later. Emma plans to finish her book on July 15. Who plans to finish first? Justify your answer with a calculation.

Hints

- First find Lucas's ending date. - How many days are in May and June? - Compare Lucas's date with Emma's date. - Which date comes first on the calendar?

Solution

1. May has \(31\) days, so there are \(31 - 25 = 6\) days after May 25 in May. 2. Subtract those days: \(50 - 6 = 44\) days remain. 3. June has \(30\) days, so \(44 - 30 = 14\) days remain. 4. Lucas plans to finish on July 14. 5. July 14 comes before July 15, so Lucas plans to finish first.

Answer

Lucas plans to finish first. He will finish on July 14, one day before Emma.
5190893
A circus performs in town every day from September 28 through October 6. On how many days are there performances altogether?

Hints

- How many days are in September? - Count the days in September, then add the days in October. - Include both the first and last performance dates.

Solution

1. September has \(30\) days. 2. Count September 28, 29, and 30: \(30 - 28 + 1 = 3\) days. 3. Count October 1 through October 6: \(6\) days. 4. Add the days: \(3 + 6 = 9\) days.

Answer

There are performances on \(9\) days.
5190903
A class reading project ends on May 4, exactly \(2\) weeks after it began. On what date did the project begin?

Hints

- How many days are in \(2\) weeks? - Which month comes before May? - Count back \(14\) days from the ending date.

Solution

1. Convert weeks to days: \(2 \times 7 = 14\) days. 2. Count back \(14\) days from May 4. Four days back is April 30, and \(10\) more days back is April 20.

Answer

The project began on April 20.
5190983
Class 3B begins an art project on May 24. The project lasts \(12\) days, and May 24 is counted as the first project day. a) How many project days are in May? b) On what date does the project end?

Hints

- How many days are in May? - Count from the start date through the end of May, including May 24. - Subtract to find how many project days remain in June.

Solution

1. May has \(31\) days. 2. Count May 24 through May 31: \(31 - 24 + 1 = 8\) project days in May. 3. Find the remaining days: \(12 - 8 = 4\) days. 4. The next four project days are June 1, 2, 3, and 4, so the project ends on June 4.

Answer

a) \(8\) days b) June 4
5190993
A circus performs in town for \(18\) days. The last performance is on July 5. a) How many performance days are in July? b) On what date did the circus give its first performance?

Hints

- First count the performance days in July. - Find how many of the \(18\) days must be in June. - How many days are in June? - Count backward through the final days of June, including both endpoints.

Solution

1. July 1 through July 5 account for \(5\) performance days. 2. The number of performance days in June is \(18 - 5 = 13\). 3. June has \(30\) days. 4. The final \(13\) days of June begin on day \(30 - 13 + 1 = 18\), so the first performance was June 18.

Answer

a) \(5\) days b) June 18
5191033
Lucas starts cleaning his room at \(3{:}35\) p.m. and finishes at \(4{:}15\) p.m. How many minutes does he spend cleaning?

Hints

- First find the minutes to the next hour. - Then add the minutes after the hour. - You may also count the whole interval forward in one step.

Solution

1. From \(3{:}35\) p.m. to \(4{:}00\) p.m. is \(60 - 35 = 25\) minutes. 2. From \(4{:}00\) p.m. to \(4{:}15\) p.m. is \(15\) minutes. 3. Add the intervals: \(25\,\text{min} + 15\,\text{min} = 40\,\text{min}\).

Answer

Lucas spends \(40\) minutes cleaning.
5191053
An adventure trip began on August 28 and ended on October 12. How many days elapsed from the start of the trip to the end?

Hints

- How many days are in August and September? - Find how many days elapsed after the start date in August. - Add the portions from each month.

Solution

1. August has \(31\) days, so \(31 - 28 = 3\) days elapsed after August 28 in August. 2. September contributes \(30\) days. 3. October contributes \(12\) days through October 12. 4. Add the intervals: \(3 + 30 + 12 = 45\) days.

Answer

\(45\) days elapsed.
5191063
Two spring camps are held on different dates. The first camp runs from March 15 through April 20. The second camp runs from May 1 through June 5. Which camp lasts more days? Support your answer by comparing the numbers of days.

Hints

- Find the number of days in each camp separately. - March and May each have \(31\) days. - Compare the two totals.

Solution

1. For the first camp, count March 15 through March 31: \(31 - 15 + 1 = 17\) days. Add \(20\) days in April: \(17 + 20 = 37\) days. 2. For the second camp, May contributes \(31\) days and June contributes \(5\) days: \(31 + 5 = 36\) days. 3. Since \(37 > 36\), the first camp lasts longer.

Answer

The first camp lasts longer: \(37\) days compared with \(36\) days.
5191243
A soccer game begins at \(10{:}15\) a.m. The first half lasts \(45\) minutes, followed by a \(15\)-minute halftime break. At what time does the second half begin?

Hints

- First find when the first half ends. - Count from \(10{:}15\) a.m. to the next hour. - Add the halftime break after the first half.

Solution

1. Add the first-half time: \(10{:}15\) a.m. plus \(45\) minutes is \(11{:}00\) a.m. 2. Add the halftime break: \(11{:}00\) a.m. plus \(15\) minutes is \(11{:}15\) a.m.

Answer

The second half begins at \(11{:}15\) a.m.
5191253
Lena puts a cake in the oven at \(3{:}50\) p.m. It must bake for \(55\) minutes and then cool for \(20\) minutes before she cuts it. At what time can Lena cut the cake?

Hints

- Find the total baking and cooling time. - Count to the next hour first if that helps. - Convert the total waiting time to hours and minutes.

Solution

1. Find the total waiting time: \(55\,\text{min} + 20\,\text{min} = 75\,\text{min}\), or \(1\) hour \(15\) minutes. 2. Add the duration to the start time: \(3{:}50\) p.m. plus \(1\) hour \(15\) minutes is \(5{:}05\) p.m.

Answer

Lena can cut the cake at \(5{:}05\) p.m.
5201153
A hiking group plans two stages. The first stage takes \(3\) hours \(20\) minutes. The second stage takes \(50\) minutes less than the first. How long does the second stage take?

Hints

- What operation does “less than” indicate? - Subtract the time in two steps. - First count back to a whole hour, then subtract the remaining minutes. - Remember that \(1\) hour is \(60\) minutes.

Solution

1. Start with \(3\) hours \(20\) minutes and subtract \(50\) minutes. 2. Subtract \(20\) minutes to reach \(3\) hours. Then \(30\) minutes still need to be subtracted. 3. Subtract the remaining \(30\) minutes: \(3\) hours minus \(30\) minutes is \(2\) hours \(30\) minutes.

Answer

The second stage takes \(2\) hours \(30\) minutes.
5201243
A soccer game begins at \(3{:}30\) p.m. The first half lasts \(45\) minutes, halftime lasts \(15\) minutes, and the second half lasts another \(45\) minutes. At what time does the game end?

Hints

- First find the total number of minutes in both halves and halftime. - How many minutes are in \(1\) hour? - Add the full hour first, then the remaining minutes.

Solution

1. Find the total time: \(45\,\text{min} + 15\,\text{min} + 45\,\text{min} = 105\,\text{min}\). 2. Convert the duration: \(105\,\text{min} = 1\) hour \(45\) minutes. 3. Add the duration to the start time: \(3{:}30\) p.m. plus \(1\) hour \(45\) minutes is \(5{:}15\) p.m.

Answer

The soccer game ends at \(5{:}15\) p.m.
5201253
Lucas and Sarah meet at the library. Lucas arrives at \(2{:}45\) p.m. and stays for \(90\) minutes. Sarah arrives at \(3{:}15\) p.m. and reads for exactly \(1\) hour. Who leaves the library later? Justify your answer with calculations.

Hints

- Find each person's leaving time separately. - How many hours and minutes are in \(90\) minutes? - Compare the two leaving times.

Solution

1. Convert Lucas's stay: \(90\,\text{min} = 1\) hour \(30\) minutes. Adding that to \(2{:}45\) p.m. gives \(4{:}15\) p.m. 2. Add Sarah's reading time: \(3{:}15\) p.m. plus \(1\) hour is \(4{:}15\) p.m. 3. The ending times are the same.

Answer

Both leave the library at \(4{:}15\) p.m. Neither leaves later.
5201283
A field-trip bus leaves school at \(8{:}20\) a.m. The ride to the zoo takes \(1\) hour \(15\) minutes. After arriving, the students take a \(30\)-minute break before their tour begins. At what time does the tour begin?

Hints

- First find the arrival time at the zoo. - Then add the break time. - Split the minutes at the next hour if that makes the addition easier.

Solution

1. After \(1\) hour, it is \(9{:}20\) a.m. 2. After another \(15\) minutes, the bus arrives at \(9{:}35\) a.m. 3. Add the \(30\)-minute break: the tour begins at \(10{:}05\) a.m.

Answer

The tour begins at \(10{:}05\) a.m.
5201343
A hiking group starts at the base of a mountain at \(8{:}30\) a.m. and reaches the summit at \(2{:}15\) p.m. How long does the hike take?

Hints

- Break the interval into smaller parts. - Count from the starting time to the next hour. - Count the full hours, then the remaining minutes. - Add all the parts.

Solution

1. From \(8{:}30\) a.m. to \(9{:}00\) a.m. is \(30\) minutes. 2. From \(9{:}00\) a.m. to \(2{:}00\) p.m. is \(5\) hours. 3. From \(2{:}00\) p.m. to \(2{:}15\) p.m. is \(15\) minutes. 4. Add the intervals: \(5\) hours plus \(30\) minutes plus \(15\) minutes equals \(5\) hours \(45\) minutes.

Answer

The hike takes \(5\) hours \(45\) minutes.
5201353
Lisa reads from \(3{:}45\) p.m. to \(5{:}10\) p.m. Tom reads on the same day from \(4{:}20\) p.m. to \(6{:}00\) p.m. Who reads longer? Find the difference in minutes.

Hints

- Find each person's reading time separately. - Convert each duration to minutes. - How many minutes are in \(1\) hour? - Compare the two totals.

Solution

1. Lisa reads for \(15\) minutes to \(4{:}00\) p.m., \(1\) hour to \(5{:}00\) p.m., and \(10\) more minutes, for \(85\) minutes total. 2. Tom reads for \(40\) minutes to \(5{:}00\) p.m. and \(1\) more hour, for \(100\) minutes total. 3. Since \(100 > 85\), Tom reads longer. 4. The difference is \(100\,\text{min} - 85\,\text{min} = 15\,\text{min}\).

Answer

Tom reads longer by \(15\) minutes.
5201383
A regional train leaves a station at \(9{:}55\) a.m. and arrives at \(12{:}15\) p.m. How long is the train ride? Give the answer in hours and minutes.

Hints

- Count from the departure time to the next hour. - Count the full hours between the times. - Add the remaining minutes.

Solution

1. From \(9{:}55\) a.m. to \(10{:}00\) a.m. is \(5\) minutes. 2. From \(10{:}00\) a.m. to \(12{:}00\) p.m. is \(2\) hours. 3. From \(12{:}00\) p.m. to \(12{:}15\) p.m. is \(15\) minutes. 4. Add the intervals: \(2\) hours plus \(5\) minutes plus \(15\) minutes equals \(2\) hours \(20\) minutes.

Answer

The train ride lasts \(2\) hours \(20\) minutes.
5201393
Two friends visit a swimming pool. Lucas arrives at \(2{:}10\) p.m. and leaves at \(4{:}35\) p.m. Marie arrives at \(2{:}45\) p.m. and leaves at \(5{:}20\) p.m. Who stays at the pool longer?

Hints

- Find each person's time at the pool separately. - Count through whole hours if helpful. - Compare the two durations.

Solution

1. Lucas stays from \(2{:}10\) p.m. to \(4{:}35\) p.m., which is \(2\) hours \(25\) minutes. 2. Marie stays from \(2{:}45\) p.m. to \(5{:}20\) p.m., which is \(2\) hours \(35\) minutes. 3. Since \(2\) hours \(35\) minutes is longer than \(2\) hours \(25\) minutes, Marie stays longer.

Answer

Marie stays at the pool longer.
5201443
The Meyer family visits a zoo. They enter at \(10{:}10\) a.m. and leave at \(2{:}40\) p.m. How long are they at the zoo?

Hints

- Identify the starting and ending times. - Count the full hours first. - Then add the remaining minutes. - A time line may help.

Solution

1. From \(10{:}10\) a.m. to \(2{:}10\) p.m. is \(4\) hours. 2. From \(2{:}10\) p.m. to \(2{:}40\) p.m. is \(30\) minutes. 3. The total time is \(4\) hours \(30\) minutes.

Answer

The family is at the zoo for \(4\) hours \(30\) minutes.
5201453
A large loaf of bread must bake for \(80\) minutes. Mrs. Smith puts it in the oven at \(11{:}45\) a.m. At what time should she take it out?

Hints

- How many hours and minutes are in \(80\) minutes? - What time is it one hour after the bread goes in? - How many minutes are there from the starting time to the next full hour? - Add the remaining minutes in steps.

Solution

1. Convert the baking time: \(80\,\text{min} = 1\) hour \(20\) minutes. 2. Add \(1\) hour to \(11{:}45\) a.m. to get \(12{:}45\) p.m. 3. Add the remaining \(20\) minutes to get \(1{:}05\) p.m.

Answer

Mrs. Smith should take the bread out at \(1{:}05\) p.m.
5201483
A movie at school begins at \(3{:}20\) p.m. and ends at \(5{:}05\) p.m. How long is the movie? Give the answer in hours and minutes.

Hints

- Count from the start time to the next hour. - Count the full hour between the times. - Add the final few minutes.

Solution

1. From \(3{:}20\) p.m. to \(4{:}00\) p.m. is \(40\) minutes. 2. From \(4{:}00\) p.m. to \(5{:}00\) p.m. is \(1\) hour. 3. From \(5{:}00\) p.m. to \(5{:}05\) p.m. is \(5\) minutes. 4. Add the intervals: \(1\) hour plus \(40\) minutes plus \(5\) minutes equals \(1\) hour \(45\) minutes.

Answer

The movie lasts \(1\) hour \(45\) minutes.
5201513
A city bus leaves the station at \(1{:}45\) p.m. It travels through three sections of its route: - The first section takes \(8\) minutes. - The second section takes \(12\) minutes. - The final section takes \(6\) minutes. At what time does the bus reach the end of the route?

Hints

- Add the three travel times first. - Add the total travel time to the departure time. - Pay attention to crossing into the next hour.

Solution

1. Find the total travel time: \(8\,\text{min} + 12\,\text{min} + 6\,\text{min} = 26\,\text{min}\). 2. From \(1{:}45\) p.m. to \(2{:}00\) p.m. is \(15\) minutes, leaving \(26 - 15 = 11\) minutes. 3. Add the remaining \(11\) minutes. The bus arrives at \(2{:}11\) p.m.

Answer

The bus reaches the end of the route at \(2{:}11\) p.m.
5201533
Lisa and Tom have a reading challenge. Lisa begins at \(2{:}30\) p.m. and reads for exactly \(45\) minutes. Tom begins at \(2{:}45\) p.m. and stops at \(3{:}40\) p.m. Who reads longer? What is the difference in minutes?

Hints

- Find each person's reading time. - For Tom, count to the next hour and then to the ending time. - Compare the durations in minutes. - Subtract to find the difference.

Solution

1. Lisa reads for \(45\) minutes. 2. Tom reads \(15\) minutes from \(2{:}45\) p.m. to \(3{:}00\) p.m. and another \(40\) minutes to \(3{:}40\) p.m., for \(55\) minutes total. 3. Since \(55 > 45\), Tom reads longer. 4. The difference is \(55\,\text{min} - 45\,\text{min} = 10\,\text{min}\).

Answer

Tom reads \(10\) minutes longer than Lisa.
5205833
Find how many hours and minutes have elapsed since midnight at each time: a) \(8{:}40\) a.m. b) \(2{:}15\) p.m. c) \(9{:}05\) p.m.

Hints

- Think about how many hours have passed since midnight. - For an afternoon or evening time, include the \(12\) hours from midnight to noon. - A new day begins at midnight.

Solution

1. Midnight is the beginning of the day. 2. At \(8{:}40\) a.m., \(8\) hours \(40\) minutes have elapsed. 3. At \(2{:}15\) p.m., \(12\) hours plus \(2\) hours \(15\) minutes have elapsed, for \(14\) hours \(15\) minutes. 4. At \(9{:}05\) p.m., \(12\) hours plus \(9\) hours \(5\) minutes have elapsed, for \(21\) hours \(5\) minutes.

Answer

a) \(8\) hours \(40\) minutes b) \(14\) hours \(15\) minutes c) \(21\) hours \(5\) minutes
5205843
Clock A shows \(11{:}15\) a.m. Clock B shows \(3{:}40\) p.m. How much time passes between the two times?

Hints

- Count the full hours between the times. - Then add the remaining minutes. - You can also count to the next hour first.

Solution

1. From \(11{:}15\) a.m. to \(3{:}15\) p.m. is \(4\) hours. 2. From \(3{:}15\) p.m. to \(3{:}40\) p.m. is \(25\) minutes. 3. The total interval is \(4\) hours \(25\) minutes.

Answer

\(4\) hours \(25\) minutes
5206023
Emma goes to practice at \(4{:}45\) p.m. The practice lasts \(1\) hour \(50\) minutes. At what time does it end?

Hints

- Add the duration in two steps. - First add the full hour. - Count to the next hour, then add the remaining minutes. - Picture moving the hands forward on a clock.

Solution

1. Add \(1\) hour to \(4{:}45\) p.m. to get \(5{:}45\) p.m. 2. Add \(15\) minutes to reach \(6{:}00\) p.m. There are \(50 - 15 = 35\) minutes left. 3. Add the remaining \(35\) minutes. Practice ends at \(6{:}35\) p.m.

Answer

Practice ends at \(6{:}35\) p.m.
5206043
A hiking group starts at \(10{:}35\) a.m. and hikes for \(3\) hours \(45\) minutes. At what time does the hike end?

Hints

- How many minutes are in \(1\) hour? - Add the full hours first. - Count to the next hour, then add the remaining minutes. - Split the \(45\) minutes at the hour change.

Solution

1. Add \(3\) hours: \(10{:}35\) a.m. becomes \(1{:}35\) p.m. 2. Of the \(45\) minutes, \(25\) minutes reach \(2{:}00\) p.m., leaving \(20\) minutes. 3. Add the remaining \(20\) minutes. The hike ends at \(2{:}20\) p.m.

Answer

The hike ends at \(2{:}20\) p.m.
5206113
A baker puts bread in the oven at \(3{:}50\) a.m. The bread bakes for \(55\) minutes and then cools for \(2\) hours \(15\) minutes before it can be sold. At what time is the bread ready to sell?

Hints

- First find when the bread comes out of the oven. - Then add the cooling time. - Count to the next hour when helpful.

Solution

1. Add the baking time: \(3{:}50\) a.m. plus \(55\) minutes is \(4{:}45\) a.m. 2. Add the cooling time: \(4{:}45\) a.m. plus \(2\) hours \(15\) minutes is \(7{:}00\) a.m.

Answer

The bread is ready to sell at \(7{:}00\) a.m.
5206123
A family begins a bike trip at \(10{:}30\) a.m. The first part takes \(1\) hour \(45\) minutes. Then the family takes a \(30\)-minute break. The final part takes \(1\) hour \(10\) minutes. How long is the outing, including the break? At what time does the family arrive?

Hints

- Add all the minutes and convert any group of \(60\) minutes to an hour. - Find the total outing time, including the break. - Add the total duration to the starting time.

Solution

1. Add the time intervals: \(1\) hour \(45\) minutes plus \(30\) minutes plus \(1\) hour \(10\) minutes. 2. The minutes total \(45 + 30 + 10 = 85\) minutes, or \(1\) hour \(25\) minutes. 3. Combining that extra hour with the two given hours gives \(3\) hours \(25\) minutes. 4. Add the duration to the start time: \(10{:}30\) a.m. plus \(3\) hours \(25\) minutes is \(1{:}55\) p.m.

Answer

The outing lasts \(3\) hours \(25\) minutes, and the family arrives at \(1{:}55\) p.m.
5206223
A school bus leaves a stop at \(2{:}52\) p.m. and arrives at school at \(3{:}17\) p.m. How many minutes does the ride take?

Hints

- Count to the next hour first. - Then count from the hour to the arrival time. - Add the two shorter intervals.

Solution

1. From \(2{:}52\) p.m. to \(3{:}00\) p.m. is \(8\) minutes. 2. From \(3{:}00\) p.m. to \(3{:}17\) p.m. is \(17\) minutes. 3. Add the intervals: \(8\,\text{min} + 17\,\text{min} = 25\,\text{min}\).

Answer

The ride takes \(25\) minutes.
5206353
A researcher studies the history of two ships. The “Sunbeam” was in service from the beginning of 1925 to the beginning of 1958. The “Sea Breeze” was in service from the beginning of 1932 to the beginning of 1961. Which ship was in service longer?

Hints

- Find each ship's time in service separately. - Subtract each starting year from its ending year. - Compare the two durations.

Solution

1. Find the Sunbeam's time in service: \(1958 - 1925 = 33\) years. 2. Find the Sea Breeze's time in service: \(1961 - 1932 = 29\) years. 3. Compare the durations: \(33 > 29\). The Sunbeam was in service longer.

Answer

The Sunbeam was in service longer. It served for \(33\) years, compared with \(29\) years for the Sea Breeze.
5207123
A hiker starts a trail at \(9{:}45\) a.m. The planned hiking time is \(3\) hours \(15\) minutes. During the hike, the hiker also takes an extra \(25\)-minute picnic break. a) What time would the hiker arrive without the extra break? b) What time does the hiker actually arrive? c) Suppose the hiker started at \(10{:}00\) a.m. but skipped the break. Would the hiker arrive earlier or later than in part b)? Explain.

Hints

- Add the hiking time to the starting time first. - For part b), add the break after finding the arrival time without it. - Picture the times on a clock face or time line if needed. - For part c), calculate the new arrival time and compare it with part b).

Solution

1. Add the planned hiking time to the original start time. From \(9{:}45\) a.m., adding \(3\) hours gives \(12{:}45\) p.m., and adding \(15\) minutes gives \(1{:}00\) p.m. 2. Add the \(25\)-minute break: \(1{:}00\) p.m. plus \(25\) minutes is \(1{:}25\) p.m. 3. With a \(10{:}00\) a.m. start and no break, adding \(3\) hours \(15\) minutes gives \(1{:}15\) p.m. This is \(10\) minutes earlier than \(1{:}25\) p.m.

Answer

a) \(1{:}00\) p.m. b) \(1{:}25\) p.m. c) Earlier. The hiker would arrive at \(1{:}15\) p.m., which is \(10\) minutes earlier than in part b).
5207133
A bus stop lists these afternoon departure times: Route A: \(1{:}55\) p.m. Route B: \(3{:}10\) p.m. Route C: \(5{:}05\) p.m. a) How many minutes are there between the departures of Route A and Route B? b) A passenger arrives at \(4{:}40\) p.m. How many minutes must the passenger wait for Route C? c) Route B is running \(18\) minutes late today. What time will it actually leave?

Hints

- Count to the next hour, then continue to the later time. - For part b), find the elapsed time from the arrival time to Route C's departure. - A delay is added to the scheduled departure time.

Solution

1. From \(1{:}55\) p.m. to \(2{:}00\) p.m. is \(5\) minutes. From \(2{:}00\) p.m. to \(3{:}10\) p.m. is \(70\) minutes. The total is \(5 + 70 = 75\) minutes. 2. From \(4{:}40\) p.m. to \(5{:}00\) p.m. is \(20\) minutes, and from \(5{:}00\) p.m. to \(5{:}05\) p.m. is \(5\) minutes. The wait is \(25\) minutes. 3. Add the delay: \(3{:}10\) p.m. plus \(18\) minutes is \(3{:}28\) p.m.

Answer

a) \(75\) minutes b) \(25\) minutes c) \(3{:}28\) p.m.
5209163
A young apple tree is planted in a school garden on March 15. The gardener says the tree should receive its first fertilizer exactly 5 months and 12 days later. On what date should the tree be fertilized?

Hints

- First count forward the full number of months. - Then count forward the remaining days. - What month is 5 months after March?

Solution

1. Count forward 5 months from March 15: April 15, May 15, June 15, July 15, and August 15. 2. Count forward 12 more days from August 15: August 27. 3. The tree should be fertilized on August 27.

Answer

The apple tree should be fertilized on August 27.
5210053
Three children trained for a city race. - Mia trained from \(3{:}55\) p.m. to \(5{:}15\) p.m. - Liam trained from \(4{:}10\) p.m. to \(5{:}28\) p.m. - Sofia trained from \(4{:}05\) p.m. to \(5{:}22\) p.m. Find each training time in minutes. Then list the children from shortest training time to longest.

Hints

- Find each child's training time separately. - One hour has \(60\) minutes. - Compare the three durations after you calculate them.

Solution

1. Mia trained for \(5\) minutes to \(4{:}00\) p.m. and then \(75\) more minutes, for a total of \(80\) minutes. 2. Liam trained for \(60\) minutes to \(5{:}10\) p.m. and then \(18\) more minutes, for a total of \(78\) minutes. 3. Sofia trained for \(60\) minutes to \(5{:}05\) p.m. and then \(17\) more minutes, for a total of \(77\) minutes. 4. Compare: \(77 < 78 < 80\).

Answer

Shortest to longest: Sofia (\(77\,\text{min}\)), Liam (\(78\,\text{min}\)), Mia (\(80\,\text{min}\)).
5210193
A movie starts at \(3{:}45\) p.m. and ends at \(6{:}20\) p.m. There is a \(15\)-minute intermission. What is the movie's running time, not including the intermission?

Hints

- First find the total time from the start to the end. - How does the intermission affect the time the movie is actually playing? - It may help to count to the next hour first.

Solution

1. The total time from \(3{:}45\) p.m. to \(6{:}20\) p.m. is \(2\) hours \(35\) minutes. 2. Subtract the \(15\)-minute intermission: \(2\,\text{hr}\,35\,\text{min} - 15\,\text{min} = 2\,\text{hr}\,20\,\text{min}\).

Answer

The movie's running time is \(2\,\text{hr}\,20\,\text{min}\).
5210393
On a fall day, the sun rises at \(7{:}42\) a.m. The daylight lasts exactly \(9\,\text{hr}\,55\,\text{min}\). What time does the sun set?

Hints

- Add the length of daylight to the sunrise time. - Remember that \(60\) minutes make one hour. - You can add the hours first and then the minutes.

Solution

1. Add \(9\) hours to \(7{:}42\) a.m. to get \(4{:}42\) p.m. 2. Add \(55\) minutes. From \(4{:}42\) p.m. to \(5{:}00\) p.m. is \(18\) minutes, leaving \(37\) minutes. 3. The sunset time is \(5{:}37\) p.m.

Answer

The sun sets at \(5{:}37\) p.m.
5210503
An overnight train leaves at \(11{:}20\) p.m. and is scheduled to arrive the next morning at \(6{:}40\) a.m. a) How long is the train trip? b) Construction delays the train by \(25\) minutes. What time does it arrive?

Hints

- Split the trip at midnight. - Add the delay to the scheduled arrival time. - Regroup when the minutes reach \(60\).

Solution

1. From \(11{:}20\) p.m. to midnight is \(40\) minutes. From midnight to \(6{:}40\) a.m. is \(6\) hours \(40\) minutes. 2. The total trip time is \(40\,\text{min} + 6\,\text{hr}\,40\,\text{min} = 7\,\text{hr}\,20\,\text{min}\). 3. Add the delay to the scheduled arrival: \(6{:}40\) a.m. plus \(25\) minutes is \(7{:}05\) a.m.

Answer

a) \(7\,\text{hr}\,20\,\text{min}\) b) \(7{:}05\) a.m.
5210703
Roadwork on School Street begins on April 14 and ends on May 22. Both the first day and the last day count. How many days does the roadwork last?

Hints

- How many days are in April? - Remember to count the starting day. - Count the days in each month separately, then add.

Solution

1. April has \(30\) days. Counting April 14 through April 30 gives \(30 - 14 + 1 = 17\) days. 2. Counting May 1 through May 22 gives \(22\) days. 3. The total is \(17 + 22 = 39\) days.

Answer

The roadwork lasts \(39\) days.
5210713
Liam and Sarah compare the lengths of their summer jobs. Liam works from July 26 through August 12. Sarah works from June 18 through July 5. For each job, count both the first and last day. Who works more days?

Hints

- Find each person's number of workdays separately. - How many days are in June and July? - Remember to count each first day.

Solution

1. July has \(31\) days. Liam works \(31 - 26 + 1 = 6\) days in July and \(12\) days in August, for \(6 + 12 = 18\) days. 2. June has \(30\) days. Sarah works \(30 - 18 + 1 = 13\) days in June and \(5\) days in July, for \(13 + 5 = 18\) days. 3. Both jobs last \(18\) days.

Answer

Neither works more days. Liam and Sarah each work \(18\) days.
5210723
A beginner sailing course lasts exactly \(24\) days and begins on July 15. The starting day counts as Day 1. What is the last day of the course?

Hints

- How many course days occur in July? - How many of the \(24\) days remain for August? - Remember that July has \(31\) days.

Solution

1. July has \(31\) days. Counting July 15 through July 31 gives \(31 - 15 + 1 = 17\) course days. 2. There are \(24 - 17 = 7\) course days left for August. 3. The seventh day in August is August 7.

Answer

The last day of the course is August 7.
5212213
Mia's swim practice starts in the pool at \(3{:}30\,\text{p.m.}\) and lasts \(90\) minutes. She must arrive at the pool \(15\) minutes before practice to change. After practice, she needs another \(20\) minutes to shower and dry her hair. a) What is the latest time Mia can arrive at the pool? b) What time will Mia be ready to leave the pool?

Hints

- Decide whether to count backward or forward for each part. - How many hours and minutes are in \(90\) minutes? - Work one time interval at a time.

Solution

1. Count back \(15\) minutes from \(3{:}30\,\text{p.m.}\): \(3{:}30\,\text{p.m.} - 15\,\text{minutes} = 3{:}15\,\text{p.m.}\). 2. Convert \(90\) minutes to \(1\) hour \(30\) minutes. Practice ends at \(3{:}30\,\text{p.m.} + 1\,\text{hour}\,30\,\text{minutes} = 5{:}00\,\text{p.m.}\). 3. Add \(20\) minutes after practice: \(5{:}00\,\text{p.m.} + 20\,\text{minutes} = 5{:}20\,\text{p.m.}\).

Answer

a) Mia must arrive by \(3{:}15\,\text{p.m.}\) b) Mia will be ready to leave at \(5{:}20\,\text{p.m.}\)
5212483
At \(3{:}00\) p.m., someone says, “More than half of the day has already passed.” Is the statement correct? Explain by finding how many hours are in half a day and how many hours have passed since midnight.

Hints

- How many hours are in a full day? - How do you find half of a number? - Count the hours from midnight to \(3{:}00\) p.m. - Compare the elapsed hours with the length of half a day.

Solution

1. A full day has \(24\) hours, so half a day is \(24 \div 2 = 12\) hours. 2. From midnight to \(3{:}00\) p.m., \(15\) hours have passed. 3. Since \(15 > 12\), more than half of the day has passed.

Answer

Yes. Half a day is \(12\) hours, and \(15\) hours have passed since midnight.
5212803
A movie begins at \(8{:}15\) p.m. 1) How much time has passed since noon? 2) How much time remains from the start of the movie until midnight?

Hints

- Break each interval into hours and minutes. - For part 2, first count from \(8{:}15\) p.m. to the next hour. - Then count the full hours from \(9{:}00\) p.m. to midnight.

Solution

1. From noon to \(8{:}00\) p.m. is \(8\) hours, and another \(15\) minutes reaches \(8{:}15\) p.m. The elapsed time is \(8\) hours \(15\) minutes. 2. From \(8{:}15\) p.m. to \(9{:}00\) p.m. is \(45\) minutes. From \(9{:}00\) p.m. to midnight is \(3\) hours. The remaining time is \(3\) hours \(45\) minutes.

Answer

1) \(8\) hours \(15\) minutes 2) \(3\) hours \(45\) minutes
5214103
A bus leaves the station at \(8{:}15\) a.m. and reaches its last stop at \(9{:}40\) a.m. How long does the bus ride take?

Hints

- Count to the next convenient hour, then add the remaining minutes. - A time line can help you combine the intervals.

Solution

1. From \(8{:}15\) a.m. to \(9{:}15\) a.m. is \(1\) hour. 2. From \(9{:}15\) a.m. to \(9{:}40\) a.m. is \(25\) minutes. 3. The total travel time is \(1\) hour \(25\) minutes.

Answer

The bus ride takes \(1\) hour \(25\) minutes.
5215093
A trail sign says a hike to a mountain lodge takes \(2\) hours \(45\) minutes. The Miller family starts at \(10{:}15\) a.m. and arrives at \(12{:}40\) p.m. How much faster did the family finish than the time shown on the sign?

Hints

- First find how long the family actually hiked. - Count the full hours and then the remaining minutes. - Compare the actual time with the time on the sign.

Solution

1. Find the actual hiking time. From \(10{:}15\) a.m. to \(12{:}15\) p.m. is \(2\) hours, and from \(12{:}15\) p.m. to \(12{:}40\) p.m. is \(25\) minutes. The hike took \(2\) hours \(25\) minutes. 2. Compare the times: \(2\) hours \(45\) minutes minus \(2\) hours \(25\) minutes is \(20\) minutes.

Answer

The family finished \(20\) minutes faster.
5215103
A movie is scheduled to last \(1\) hour \(50\) minutes. It begins at \(3{:}30\) p.m., but a technical problem stops the movie at \(5{:}10\) p.m. How many minutes of the movie were not shown?

Hints

- First find how long the movie played before it stopped. - Count to the next hour when helpful. - Compare the time shown with the movie's scheduled length.

Solution

1. Find how long the movie played. From \(3{:}30\) p.m. to \(4{:}30\) p.m. is \(1\) hour, and from \(4{:}30\) p.m. to \(5{:}10\) p.m. is \(40\) minutes. The movie played for \(1\) hour \(40\) minutes. 2. Subtract the shown time from the scheduled length: \(1\) hour \(50\) minutes minus \(1\) hour \(40\) minutes is \(10\) minutes.

Answer

\(10\) minutes of the movie were not shown.
5313473
Clocks a) and b) show two times on the same morning. Find the elapsed time between them.
Figure for problem 531347

Hints

- Read and write the time on each clock. - Count the full hour first. - Then add the remaining minutes.

Solution

1. Clock a) shows \(8{:}20\) a.m., and clock b) shows \(9{:}45\) a.m. 2. From \(8{:}20\) a.m. to \(9{:}20\) a.m. is \(1\) hour. 3. From \(9{:}20\) a.m. to \(9{:}45\) a.m. is \(25\) minutes. 4. The total elapsed time is \(1\) hour \(25\) minutes.

Answer

The elapsed time is \(1\) hour \(25\) minutes.
5313483
Lucas starts his homework at \(2{:}45\,\text{p.m.}\) He works for \(50\) minutes, takes a \(15\)-minute break, and then studies for another \(35\) minutes. What time does he finish?

Hints

- Add each time interval in order. - Pay attention when the minutes pass the next hour. - You can also add the three intervals first and then add the total to the starting time.

Solution

1. After \(50\) minutes of work, the time is \(2{:}45\,\text{p.m.} + 50\,\text{minutes} = 3{:}35\,\text{p.m.}\). 2. After the \(15\)-minute break, the time is \(3{:}35\,\text{p.m.} + 15\,\text{minutes} = 3{:}50\,\text{p.m.}\). 3. After another \(35\) minutes of studying, the time is \(3{:}50\,\text{p.m.} + 35\,\text{minutes} = 4{:}25\,\text{p.m.}\).

Answer

Lucas finishes at \(4{:}25\,\text{p.m.}\)
5313493
An overnight train leaves at \(9{:}35\) p.m. and arrives the next morning at \(6{:}12\) a.m. How long is the trip?

Hints

- Split the elapsed time at midnight. - How much time passes before midnight? - How much time passes after midnight?

Solution

1. From \(9{:}35\) p.m. to midnight is \(2\) hours \(25\) minutes. 2. From midnight to \(6{:}12\) a.m. is \(6\) hours \(12\) minutes. 3. Add the two parts: \(2\,\text{hr}\,25\,\text{min} + 6\,\text{hr}\,12\,\text{min} = 8\,\text{hr}\,37\,\text{min}\).

Answer

The trip lasts \(8\,\text{hr}\,37\,\text{min}\).
5313503
Look at the time shown on the clock. a) What time was it exactly \(25\) minutes earlier? b) What time will it be \(45\) minutes later?
Figure for problem 531350

Hints

- Read the clock first. - Move backward on the clock for part a). - Move forward on the clock for part b).

Solution

1. The clock shows \(10{:}10\). 2. For part a), count back \(10\) minutes to \(10{:}00\), then count back the remaining \(15\) minutes. The time was \(9{:}45\). 3. For part b), add \(45\) minutes to \(10{:}10\). The time will be \(10{:}55\).

Answer

a) \(9{:}45\) b) \(10{:}55\)
5313543
At a movie theater, the previews begin at \(3{:}30\,\text{p.m.}\) and last \(15\) minutes. The movie that follows is \(102\) minutes long. What time does the entire showing end?

Hints

- First find when the movie itself begins. - Convert \(102\) minutes to hours and minutes. - Then count forward from the movie's starting time.

Solution

1. The movie begins after the \(15\)-minute preview: \(3{:}30\,\text{p.m.} + 15\,\text{minutes} = 3{:}45\,\text{p.m.}\). 2. Convert the movie's length: \(102\) minutes is \(1\) hour \(42\) minutes. 3. Add the movie's length to its start time: \(3{:}45\,\text{p.m.} + 1\,\text{hour}\,42\,\text{minutes} = 5{:}27\,\text{p.m.}\).

Answer

The entire showing ends at \(5{:}27\,\text{p.m.}\)
5313553
A hiking group starts at \(8{:}20\) a.m. and reaches its destination at \(5{:}05\) p.m. The group takes three \(20\)-minute breaks. How long is the group actually walking?

Hints

- First find the total time from start to finish. - Find the total length of the three breaks. - Subtract the break time from the total time.

Solution

1. The total elapsed time from \(8{:}20\) a.m. to \(5{:}05\) p.m. is \(8\) hours \(45\) minutes. 2. The three breaks take \(3 \times 20 = 60\) minutes, or \(1\) hour. 3. Subtract the break time: \(8\,\text{hr}\,45\,\text{min} - 1\,\text{hr} = 7\,\text{hr}\,45\,\text{min}\).

Answer

The group walks for \(7\,\text{hr}\,45\,\text{min}\).
5313573
Lisa starts reading in the morning at the time shown on clock a) and stops at the time shown on clock b). How long does she read?
Figure for problem 531357

Hints

- Read the time on each clock first. - Count the full hour between the times. - Add the remaining minutes.

Solution

1. Clock a) shows \(9{:}15\) a.m., and clock b) shows \(10{:}40\) a.m. 2. From \(9{:}15\) a.m. to \(10{:}15\) a.m. is \(1\) hour. 3. From \(10{:}15\) a.m. to \(10{:}40\) a.m. is \(25\) minutes. 4. Lisa reads for \(1\) hour \(25\) minutes.

Answer

Lisa reads for \(1\) hour \(25\) minutes.
5313583
Lucas begins a bike ride at \(1{:}50\,\text{p.m.}\) and reaches his destination at \(3{:}15\,\text{p.m.}\) How many minutes does the ride take?

Hints

- First count to the next full hour. - Remember that \(1\) hour is \(60\) minutes. - Add the separate time intervals.

Solution

1. From \(1{:}50\,\text{p.m.}\) to \(2{:}00\,\text{p.m.}\) is \(10\) minutes. 2. From \(2{:}00\,\text{p.m.}\) to \(3{:}00\,\text{p.m.}\) is \(60\) minutes. 3. From \(3{:}00\,\text{p.m.}\) to \(3{:}15\,\text{p.m.}\) is \(15\) minutes. 4. Add the intervals: \(10 + 60 + 15 = 85\) minutes.

Answer

The bike ride takes \(85\) minutes.
5313633
Tim's soccer practice starts at \(3{:}30\) p.m. The clock shows when practice ends. How many minutes does practice last?
Figure for problem 531363

Hints

- Read the ending time on the clock. - Count to the next hour, then add the remaining minutes.

Solution

1. The clock shows an ending time of \(4{:}15\) p.m. 2. From \(3{:}30\) p.m. to \(4{:}00\) p.m. is \(30\) minutes. 3. From \(4{:}00\) p.m. to \(4{:}15\) p.m. is \(15\) minutes. 4. The total is \(30 + 15 = 45\) minutes.

Answer

Practice lasts \(45\) minutes.
5313643
A movie showing begins at \(5{:}30\,\text{p.m.}\) The previews last \(15\) minutes, and the movie lasts \(105\) minutes. What time does the entire showing end?

Hints

- First add the preview time and the movie time. - How many hours are in \(120\) minutes? - Add that amount of time to the starting time.

Solution

1. Add the previews and movie lengths: \(15 + 105 = 120\) minutes. 2. Convert \(120\) minutes to \(2\) hours. 3. Count forward \(2\) hours from \(5{:}30\,\text{p.m.}\) The showing ends at \(7{:}30\,\text{p.m.}\)

Answer

The showing ends at \(7{:}30\,\text{p.m.}\)
5314113
Read the time on each clock. How many minutes pass from clock a) to clock b)? Both times are in the same afternoon.
Figure for problem 531411

Hints

- Read the hour and minute hands on both clocks. - Find the time from clock a) to the next matching minute after the hour. - Add the remaining minutes.

Solution

1. Clock a) shows \(2{:}10\) p.m. 2. Clock b) shows \(3{:}45\) p.m. 3. From \(2{:}10\) p.m. to \(3{:}10\) p.m. is \(60\) minutes, and from \(3{:}10\) p.m. to \(3{:}45\) p.m. is \(35\) minutes. 4. The elapsed time is \(60 + 35 = 95\) minutes.

Answer

\(95\) minutes pass.
5314203
How many minutes pass between the times on clocks a) and b)?
Figure for problem 531420

Hints

- Read both clocks. - Count from the first time to \(12{:}00\). - Add the minutes from \(12{:}00\) to the second time.

Solution

1. Clock a) shows \(11{:}50\). 2. Clock b) shows \(12{:}15\). 3. From \(11{:}50\) to \(12{:}00\) is \(10\) minutes. 4. From \(12{:}00\) to \(12{:}15\) is \(15\) minutes. 5. Add the intervals: \(10 + 15 = 25\) minutes.

Answer

\(25\) minutes pass.
5314243
The clock shows the current time in the afternoon. What time was it exactly \(1\) hour \(25\) minutes earlier?
Figure for problem 531424

Hints

- Read the time shown on the clock and count backward. - Subtract the full hour first, then subtract the minutes.

Solution

1. The clock shows \(4{:}10\,\text{p.m.}\) 2. Count back \(1\) hour to \(3{:}10\,\text{p.m.}\) 3. Count back \(25\) more minutes. From \(3{:}10\,\text{p.m.}\) to \(3{:}00\,\text{p.m.}\) is \(10\) minutes, and \(15\) more minutes back gives \(2{:}45\,\text{p.m.}\)

Answer

It was \(2{:}45\,\text{p.m.}\)
5314253
The clock at a parking garage shows the time when you enter. You leave your car there for exactly \(4\) hours \(50\) minutes. What time do you leave the garage?
Figure for problem 531425

Hints

- Read the starting time from the clock. - Add the hours first and then the minutes. - Watch for the hour changing when you add the minutes.

Solution

1. The clock shows \(10{:}15\,\text{a.m.}\) 2. Count forward \(4\) hours to \(2{:}15\,\text{p.m.}\) 3. Count forward \(50\) more minutes to \(3{:}05\,\text{p.m.}\)

Answer

You leave the garage at \(3{:}05\,\text{p.m.}\)
5314263
The clocks show three times in order during the same day. Find the elapsed time from clock A to clock B and from clock B to clock C.
Figure for problem 531426

Hints

- Read each clock carefully. - Find each elapsed time separately. - You can break an interval at a full hour or at noon.

Solution

1. Clock A shows \(7{:}15\) a.m., clock B shows \(10{:}40\) a.m., and clock C shows \(2{:}05\) p.m. 2. From \(7{:}15\) a.m. to \(10{:}15\) a.m. is \(3\) hours, and from \(10{:}15\) a.m. to \(10{:}40\) a.m. is \(25\) minutes. The elapsed time from A to B is \(3\,\text{hr}\,25\,\text{min}\). 3. From \(10{:}40\) a.m. to noon is \(1\) hour \(20\) minutes, and from noon to \(2{:}05\) p.m. is \(2\) hours \(5\) minutes. The elapsed time from B to C is \(3\,\text{hr}\,25\,\text{min}\).

Answer

A to B: \(3\,\text{hr}\,25\,\text{min}\) B to C: \(3\,\text{hr}\,25\,\text{min}\)
5314273
Look at the two clocks. Both times are in the afternoon. How much time passes from clock a) to clock b)? Give the answer in hours and minutes.
Figure for problem 531427

Hints

- Read each clock first. - Count the full hours between the two times. - Determine how many additional minutes are needed to reach the ending time. - You can also count to the next full hour first.

Solution

1. Clock a) shows \(2{:}20\) p.m. 2. Clock b) shows \(3{:}55\) p.m. 3. From \(2{:}20\) p.m. to \(3{:}20\) p.m. is \(1\) hour. 4. From \(3{:}20\) p.m. to \(3{:}55\) p.m. is \(35\) minutes. 5. The total elapsed time is \(1\) hour \(35\) minutes.

Answer

\(1\) hour \(35\) minutes pass.
5314283
The clock shows the afternoon starting time of a soccer practice. Practice ends at \(5{:}15\) p.m. How many minutes does practice last?
Figure for problem 531428

Hints

- Read the starting time on the clock. - Count to the next hour first. - Add the minutes from the hour to the ending time.

Solution

1. The clock shows \(4{:}30\) p.m. 2. From \(4{:}30\) p.m. to \(5{:}00\) p.m. is \(30\) minutes. 3. From \(5{:}00\) p.m. to \(5{:}15\) p.m. is \(15\) minutes. 4. Add the intervals: \(30 + 15 = 45\) minutes.

Answer

Practice lasts \(45\) minutes.
5314293
The clock shows the current morning time. Lunch begins in exactly \(25\) minutes. What time will lunch begin? Write the time digitally.
Figure for problem 531429

Hints

- Read the current time. - Count to the next hour first. - Add the remaining part of the \(25\) minutes.

Solution

1. The clock shows \(11{:}50\) a.m. 2. Add \(10\) minutes to reach \(12{:}00\) noon. 3. Add the remaining \(15\) minutes to reach \(12{:}15\) p.m.

Answer

Lunch begins at \(12{:}15\) p.m.
5314303
Tim's afternoon soccer practice starts at the time shown on clock a) and ends at the time shown on clock b). How many minutes does practice last?
Figure for problem 531430

Hints

- Count to the next hour first. - Find the full hours and remaining minutes. - Remember that \(1\) hour equals \(60\) minutes.

Solution

1. Clock a) shows \(3{:}30\) p.m., and clock b) shows \(5{:}00\) p.m. 2. From \(3{:}30\) p.m. to \(5{:}00\) p.m. is \(1\) hour \(30\) minutes. 3. Convert the hour to minutes: \(60 + 30 = 90\) minutes.

Answer

Practice lasts \(90\) minutes.
5314313
The clock shows when a bus leaves a bus stop in the morning. The ride to the train station takes exactly \(55\) minutes. What time does the bus arrive?
Figure for problem 531431

Hints

- How many minutes are there from the departure time to the next full hour? - How much of the \(55\)-minute ride remains? - Then count forward the remaining minutes.

Solution

1. The clock shows a departure time of \(8{:}20\,\text{a.m.}\) 2. From \(8{:}20\,\text{a.m.}\) to \(9{:}00\,\text{a.m.}\) is \(40\) minutes. 3. There are \(55 - 40 = 15\) minutes left. 4. Count forward \(15\) more minutes from \(9{:}00\,\text{a.m.}\) The bus arrives at \(9{:}15\,\text{a.m.}\)

Answer

The bus arrives at \(9{:}15\,\text{a.m.}\)
5314323
A charter bus leaves in the evening at the time shown on the clock. The trip lasts \(8\) hours \(50\) minutes. What time does the bus arrive the next morning?
Figure for problem 531432

Hints

- Read the departure time on the clock. - Find how much of the trip happens before midnight. - Use the remaining trip time to find the arrival time after midnight.

Solution

1. The clock shows a departure time of \(10{:}15\) p.m. 2. From \(10{:}15\) p.m. to midnight is \(1\) hour \(45\) minutes. 3. Subtract that part from the trip time: \(8\,\text{hr}\,50\,\text{min} - 1\,\text{hr}\,45\,\text{min} = 7\,\text{hr}\,5\,\text{min}\). 4. Starting at midnight, \(7\) hours \(5\) minutes later is \(7{:}05\) a.m.

Answer

The bus arrives at \(7{:}05\) a.m.
5314343
A concert ends in the evening at the time shown on the clock. The concert, including intermission, lasts \(2\) hours \(45\) minutes. What time did the concert begin?
Figure for problem 531434

Hints

- Work backward because the ending time is given. - Subtract the whole hours first. - When subtracting the minutes, move back to the previous full hour.

Solution

1. The clock shows an ending time of \(9{:}20\) p.m. 2. Subtract \(2\) hours: \(9{:}20\) p.m. becomes \(7{:}20\) p.m. 3. Subtract \(45\) minutes. From \(7{:}20\) p.m. back to \(7{:}00\) p.m. is \(20\) minutes, with \(25\) minutes left to subtract. 4. Moving back \(25\) more minutes gives \(6{:}35\) p.m.

Answer

The concert began at \(6{:}35\) p.m.
5314353
Students work on two assignments in a row. Clock a) shows when they begin, clock b) shows when they finish the first assignment, and clock c) shows when they finish the second assignment. How many minutes do they spend on the second assignment?
Figure for problem 531435

Hints

- Read all three clocks carefully. - Which clock shows when the second assignment begins? - Find the difference between the times on clocks b) and c).

Solution

1. Clock a) shows \(9{:}15\,\text{a.m.}\), clock b) shows \(10{:}00\,\text{a.m.}\), and clock c) shows \(10{:}35\,\text{a.m.}\) 2. The second assignment begins when the first assignment ends, at \(10{:}00\,\text{a.m.}\) 3. From \(10{:}00\,\text{a.m.}\) to \(10{:}35\,\text{a.m.}\) is \(35\) minutes.

Answer

The students spend \(35\) minutes on the second assignment.
5159463
A class is planning a hike and must return to school by \(3{:}15\) p.m. The hike to a meadow takes \(1\) hour \(10\) minutes. The class rests for \(40\) minutes, and the return hike takes \(55\) minutes. What is the latest time the class can leave school?

Hints

- Add all the travel and rest times. - Work backward from the required return time. - Express the total duration in hours and minutes before counting back.

Solution

1. Find the total time: \(1\) hour \(10\) minutes plus \(40\) minutes plus \(55\) minutes is \(2\) hours \(45\) minutes. 2. Count back \(2\) hours from \(3{:}15\) p.m. to \(1{:}15\) p.m. 3. Count back another \(45\) minutes to \(12{:}30\) p.m.

Answer

The class must leave no later than \(12{:}30\) p.m.
5160933
The Rivera family is comparing two ways to travel from Philadelphia to Washington, D.C.: 1. By car: Leave at \(9{:}15\,\text{a.m.}\) and arrive at \(12{:}40\,\text{p.m.}\). 2. By train: Leave at \(10{:}05\,\text{a.m.}\) and arrive at \(12{:}12\,\text{p.m.}\). How much travel time would the family save by taking the train instead of driving?

Hints

- Find the travel time for each option separately. - In this problem, what operation represents “time saved”? - Subtract the shorter travel time from the longer travel time.

Solution

1. Find the driving time: From \(9{:}15\,\text{a.m.}\) to \(12{:}15\,\text{p.m.}\) is \(3\) hours, and from \(12{:}15\,\text{p.m.}\) to \(12{:}40\,\text{p.m.}\) is \(25\) minutes. The drive lasts \(3\,\text{hours}\,25\,\text{minutes}\). 2. Find the train time: From \(10{:}05\,\text{a.m.}\) to \(12{:}05\,\text{p.m.}\) is \(2\) hours, and from \(12{:}05\,\text{p.m.}\) to \(12{:}12\,\text{p.m.}\) is \(7\) minutes. The train ride lasts \(2\,\text{hours}\,7\,\text{minutes}\). 3. Find the difference: \(3\,\text{hours}\,25\,\text{minutes} - 2\,\text{hours}\,7\,\text{minutes} = 1\,\text{hour}\,18\,\text{minutes}\).

Answer

The family would save \(1\,\text{hour}\,18\,\text{minutes}\).
5165063
Lucas wants to take a train from Philadelphia to Baltimore to visit a museum. The museum opens at \(11{:}00\) a.m., and the walk from the Baltimore station to the museum takes \(15\) minutes. <table> <thead> <tr><th>Train</th><th>Departure from Philadelphia</th><th>Arrival in Baltimore</th></tr> </thead> <tbody> <tr><td>1</td><td>\(8{:}20\) a.m.</td><td>\(9{:}35\) a.m.</td></tr> <tr><td>2</td><td>\(9{:}20\) a.m.</td><td>\(10{:}45\) a.m.</td></tr> <tr><td>3</td><td>\(10{:}20\) a.m.</td><td>\(11{:}38\) a.m.</td></tr> </tbody> </table> Which train lets Lucas leave as late as possible and still reach the museum when it opens? How long is that train ride?

Hints

- Work backward from the museum's opening time by the walking time. - Find the latest train arrival that is not after that time. - Calculate the elapsed time from departure to arrival.

Solution

1. Lucas must arrive at the station by \(10{:}45\) a.m. because the walk takes \(15\) minutes. 2. Train 2 arrives at exactly \(10{:}45\) a.m. Train 3 arrives too late, so Train 2 is the latest possible choice. 3. From \(9{:}20\) a.m. to \(10{:}20\) a.m. is \(1\) hour, and another \(25\) minutes reaches \(10{:}45\) a.m. The ride takes \(1\) hour \(25\) minutes.

Answer

Lucas should take Train 2, departing at \(9{:}20\) a.m. The ride takes \(1\) hour \(25\) minutes.
5165073
Sarah and Tom plan to meet at Chicago Union Station. Sarah is traveling from Milwaukee, and Tom is traveling from South Bend. They want to arrive as close to the same time as possible. <table> <thead> <tr><th colspan="2">Milwaukee to Chicago</th><th colspan="2">South Bend to Chicago</th></tr> <tr><th>Departure</th><th>Arrival</th><th>Departure</th><th>Arrival</th></tr> </thead> <tbody> <tr><td>\(8{:}06\) a.m.</td><td>\(9{:}10\) a.m.</td><td>\(8{:}25\) a.m.</td><td>\(9{:}22\) a.m.</td></tr> <tr><td>\(9{:}06\) a.m.</td><td>\(10{:}05\) a.m.</td><td>\(9{:}25\) a.m.</td><td>\(10{:}12\) a.m.</td></tr> <tr><td>\(10{:}06\) a.m.</td><td>\(11{:}12\) a.m.</td><td>\(10{:}25\) a.m.</td><td>\(11{:}15\) a.m.</td></tr> </tbody> </table> Choose one train for each person so that the difference between their arrival times is as small as possible. When does each train arrive, and what is the difference in minutes?

Hints

- Focus on the arrival columns. - Compare arrival times that are close together. - Calculate each difference and choose the smallest one.

Solution

1. Compare the nearby arrival pairs: \(9{:}10\) a.m. and \(9{:}22\) a.m. differ by \(12\) minutes. 2. \(10{:}05\) a.m. and \(10{:}12\) a.m. differ by \(7\) minutes. 3. \(11{:}12\) a.m. and \(11{:}15\) a.m. differ by \(3\) minutes. 4. Arrival times from different rows differ by at least \(43\) minutes, so the smallest possible difference is \(3\) minutes.

Answer

Sarah arrives at \(11{:}12\) a.m., and Tom arrives at \(11{:}15\) a.m. The difference is \(3\) minutes.
5166143
Two trains travel between the same two cities. Train A: departs at \(7{:}12\,\text{a.m.}\) and arrives at \(11{:}48\,\text{a.m.}\). Train B: departs at \(1{:}55\,\text{p.m.}\) and arrives at \(6{:}25\,\text{p.m.}\). Train A has \(8\) passenger cars, and Train B has \(10\) passenger cars. Which train takes longer? Also find the difference in minutes.

Hints

- Find each train’s travel time separately. - Count to the next full hour, then count the full hours and remaining minutes. - Compare the two travel times. - Subtract the shorter time from the longer time.

Solution

1. Find Train A’s travel time: From \(7{:}12\,\text{a.m.}\) to \(11{:}12\,\text{a.m.}\) is \(4\) hours, and from \(11{:}12\,\text{a.m.}\) to \(11{:}48\,\text{a.m.}\) is \(36\) minutes. Train A takes \(4\,\text{hours}\,36\,\text{minutes}\). 2. Find Train B’s travel time: From \(1{:}55\,\text{p.m.}\) to \(2{:}00\,\text{p.m.}\) is \(5\) minutes, from \(2{:}00\,\text{p.m.}\) to \(6{:}00\,\text{p.m.}\) is \(4\) hours, and from \(6{:}00\,\text{p.m.}\) to \(6{:}25\,\text{p.m.}\) is \(25\) minutes. Train B takes \(4\,\text{hours}\,30\,\text{minutes}\). 3. Compare the travel times: \(4\,\text{hours}\,36\,\text{minutes} > 4\,\text{hours}\,30\,\text{minutes}\), so Train A takes longer. 4. Find the difference: \(4\,\text{hours}\,36\,\text{minutes} - 4\,\text{hours}\,30\,\text{minutes} = 6\,\text{minutes}\).

Answer

Train A takes longer by \(6\) minutes.
5166153
An observatory records the night sky from \(10{:}35\,\text{p.m.}\) until \(4{:}15\,\text{a.m.}\) the next morning. Clouds force the camera to stop recording for \(50\) minutes. For how long does the camera actually record the sky?

Hints

- How much time passes before midnight? - How much time passes after midnight? - First find the full time interval. - What should you do with the time when the camera was paused?

Solution

1. Find the time from \(10{:}35\,\text{p.m.}\) to midnight: \(1\,\text{hour}\,25\,\text{minutes}\). 2. Find the time from midnight to \(4{:}15\,\text{a.m.}\): \(4\,\text{hours}\,15\,\text{minutes}\). 3. Add the two intervals: \(1\,\text{hour}\,25\,\text{minutes} + 4\,\text{hours}\,15\,\text{minutes} = 5\,\text{hours}\,40\,\text{minutes}\). 4. Subtract the pause: \(5\,\text{hours}\,40\,\text{minutes} - 50\,\text{minutes} = 4\,\text{hours}\,50\,\text{minutes}\).

Answer

The camera records the sky for \(4\,\text{hours}\,50\,\text{minutes}\).
5169143
Tim plans to visit a friend by train. He can choose from these trains: <table> <thead> <tr> <th>Train</th> <th>Departure</th> <th>Arrival</th> </tr> </thead> <tbody> <tr> <td>Train 5</td> <td>\(7{:}12\,\text{a.m.}\)</td> <td>\(7{:}58\,\text{a.m.}\)</td> </tr> <tr> <td>Train 7</td> <td>\(8{:}12\,\text{a.m.}\)</td> <td>\(8{:}58\,\text{a.m.}\)</td> </tr> </tbody> </table> Tim must arrive by \(9{:}10\,\text{a.m.}\). It takes him \(18\) minutes to walk from home to the departure station. What is the latest time he can leave home and still catch the appropriate train?

Hints

- Which arrival is the latest one that still gets Tim there on time? - Find the departure time for that train. - Subtract Tim’s walking time from the departure time.

Solution

1. Choose the latest train that arrives before \(9{:}10\,\text{a.m.}\). The train arriving at \(8{:}58\,\text{a.m.}\) is the latest one that works. 2. That train departs at \(8{:}12\,\text{a.m.}\). 3. Subtract the walking time: \(8{:}12\,\text{a.m.} - 18\,\text{minutes} = 7{:}54\,\text{a.m.}\).

Answer

Tim must leave home by \(7{:}54\,\text{a.m.}\).
5171693
A boat travels between River City and Baytown. Because the river flows, the travel times are different in the two directions. <table> <tr> <th>Direction</th> <th>Departure</th> <th>Arrival</th> </tr> <tr> <td>River City to Baytown, downstream</td> <td>\(1{:}00\,\text{p.m.}\)</td> <td>\(2{:}30\,\text{p.m.}\)</td> </tr> <tr> <td>Baytown to River City, upstream</td> <td>\(3{:}30\,\text{p.m.}\)</td> <td>\(5{:}45\,\text{p.m.}\)</td> </tr> </table> a) Find the travel time in each direction. b) How many minutes longer is one trip than the other? c) Why does the upstream trip take longer?

Hints

- Find each elapsed time separately. - Convert both times to minutes before finding the difference. - Think about how moving against a current affects a boat.

Solution

1. Find the downstream time: From \(1{:}00\,\text{p.m.}\) to \(2{:}30\,\text{p.m.}\) is \(1\) hour \(30\) minutes, or \(90\) minutes. 2. Find the upstream time: From \(3{:}30\,\text{p.m.}\) to \(5{:}45\,\text{p.m.}\) is \(2\) hours \(15\) minutes, or \(135\) minutes. 3. Find the difference: \(135 - 90 = 45\) minutes. 4. The upstream trip takes longer because the boat travels against the river current.

Answer

a) Downstream: \(1\) hour \(30\) minutes. Upstream: \(2\) hours \(15\) minutes. b) The trips differ by \(45\) minutes. c) The upstream trip takes longer because the boat travels against the current.
5171703
Two boat lines travel from Harbor City to the lighthouse. <table> <thead> <tr> <th>Stop</th> <th>Line A</th> <th>Line B</th> </tr> </thead> <tbody> <tr> <td>Harbor City, departs</td> <td>\(8{:}15\,\text{a.m.}\)</td> <td>\(9{:}00\,\text{a.m.}\)</td> </tr> <tr> <td>Island View, departs</td> <td>\(8{:}45\,\text{a.m.}\)</td> <td>\(9{:}30\,\text{a.m.}\)</td> </tr> <tr> <td>Lighthouse, arrives</td> <td>\(9{:}25\,\text{a.m.}\)</td> <td>\(10{:}10\,\text{a.m.}\)</td> </tr> </tbody> </table> a) How long does Line A take from Harbor City to the lighthouse? b) Mr. Miller must arrive at the lighthouse by \(10{:}00\,\text{a.m.}\). Which line should he take? c) How many minutes apart are the two arrival times at the lighthouse?

Hints

- Use the departure and arrival times for Line A. - Compare each arrival time with the required arrival time. - Count forward from the earlier arrival to the later arrival.

Solution

1. Find Line A’s travel time: From \(8{:}15\,\text{a.m.}\) to \(9{:}15\,\text{a.m.}\) is \(1\) hour, and another \(10\) minutes gives \(1\) hour \(10\) minutes, or \(70\) minutes. 2. Compare the arrivals with \(10{:}00\,\text{a.m.}\). Line A arrives at \(9{:}25\,\text{a.m.}\), while Line B arrives at \(10{:}10\,\text{a.m.}\), so Mr. Miller must take Line A. 3. Find the time between arrivals: From \(9{:}25\,\text{a.m.}\) to \(10{:}10\,\text{a.m.}\) is \(45\) minutes.

Answer

a) Line A takes \(1\) hour \(10\) minutes, or \(70\) minutes. b) Mr. Miller should take Line A. c) The arrival times are \(45\) minutes apart.
5171803
Four elementary school groups go on a field-day hike. The table shows when each group leaves the school and reaches the destination: <table> <tr><th>Group</th><th>Departure</th><th>Arrival</th></tr> <tr><td>Group A</td><td>\(8{:}10\,\text{a.m.}\)</td><td>\(12{:}45\,\text{p.m.}\)</td></tr> <tr><td>Group B</td><td>\(8{:}25\,\text{a.m.}\)</td><td>\(1{:}05\,\text{p.m.}\)</td></tr> <tr><td>Group C</td><td>\(8{:}40\,\text{a.m.}\)</td><td>\(1{:}15\,\text{p.m.}\)</td></tr> <tr><td>Group D</td><td>\(8{:}55\,\text{a.m.}\)</td><td>\(1{:}35\,\text{p.m.}\)</td></tr> </table> a) Which group leaves latest? b) Which group arrives first? c) Find each group’s hiking time in hours and minutes.

Hints

- Compare all the departure times to find the latest one. - Compare all the arrival times to find the earliest one. - For each group, count from its departure time to its arrival time.

Solution

1. Compare the departure times. The latest departure is \(8{:}55\,\text{a.m.}\), so Group D leaves latest. 2. Compare the arrival times. The earliest arrival is \(12{:}45\,\text{p.m.}\), so Group A arrives first. 3. Group A: From \(8{:}10\,\text{a.m.}\) to \(12{:}45\,\text{p.m.}\) is \(4\) hours \(35\) minutes. 4. Group B: From \(8{:}25\,\text{a.m.}\) to \(1{:}05\,\text{p.m.}\) is \(4\) hours \(40\) minutes. 5. Group C: From \(8{:}40\,\text{a.m.}\) to \(1{:}15\,\text{p.m.}\) is \(4\) hours \(35\) minutes. 6. Group D: From \(8{:}55\,\text{a.m.}\) to \(1{:}35\,\text{p.m.}\) is \(4\) hours \(40\) minutes.

Answer

a) Group D b) Group A c) Group A: \(4\) hours \(35\) minutes; Group B: \(4\) hours \(40\) minutes; Group C: \(4\) hours \(35\) minutes; Group D: \(4\) hours \(40\) minutes.
5171903
Lucas plants bean seeds on May 18. His garden journal gives these time ranges for each stage of growth: <table> <tr> <th>Event</th> <th>Time after planting</th> </tr> <tr> <td>Sprouting</td> <td>\(4\) to \(6\) days</td> </tr> <tr> <td>First leaf</td> <td>\(10\) to \(14\) days</td> </tr> <tr> <td>First flower</td> <td>\(20\) to \(25\) days</td> </tr> </table> Find the date range when Lucas can expect each event. May has \(31\) days.

Hints

- Find both the earliest and latest date for each event. - May has \(31\) days. - When a sum is greater than \(31\), subtract \(31\) to find the date in June.

Solution

1. Sprouting: \(18 + 4 = 22\) and \(18 + 6 = 24\), so the range is May 22 through May 24. 2. First leaf: \(18 + 10 = 28\) and \(18 + 14 = 32\). Since May has \(31\) days, day \(32\) is June 1. The range is May 28 through June 1. 3. First flower: \(18 + 20 = 38\) and \(18 + 25 = 43\). Subtract \(31\): \(38 - 31 = 7\) and \(43 - 31 = 12\). The range is June 7 through June 12.

Answer

Sprouting: May 22 through May 24 First leaf: May 28 through June 1 First flower: June 7 through June 12
5182053
An overnight train leaves at \(9{:}45\,\text{p.m.}\) and arrives at \(6{:}15\,\text{a.m.}\) the next morning. The scheduled travel time is exactly \(8\) hours. How many minutes longer is the actual trip than the scheduled trip?

Hints

- Find the time from departure to midnight. - Find the time from midnight to arrival. - Add those intervals and compare the result with \(8\) hours.

Solution

1. Find the time from departure to midnight: From \(9{:}45\,\text{p.m.}\) to \(12{:}00\,\text{a.m.}\) is \(2\) hours \(15\) minutes. 2. Find the time after midnight: From \(12{:}00\,\text{a.m.}\) to \(6{:}15\,\text{a.m.}\) is \(6\) hours \(15\) minutes. 3. Add the intervals: \(2\,\text{hours}\,15\,\text{minutes} + 6\,\text{hours}\,15\,\text{minutes} = 8\,\text{hours}\,30\,\text{minutes}\). 4. Compare with the schedule: \(8\,\text{hours}\,30\,\text{minutes} - 8\,\text{hours} = 30\,\text{minutes}\).

Answer

The actual trip is \(30\) minutes longer than scheduled.
5182063
Use \(10\) hours of sleep as a comparison value. Lucas goes to sleep at \(8{:}30\,\text{p.m.}\) and wakes at \(7{:}15\,\text{a.m.}\). Maria goes to sleep at \(9{:}15\,\text{p.m.}\) and wakes at \(6{:}45\,\text{a.m.}\). Who sleeps longer than \(10\) hours, and who sleeps less? Find each difference in minutes.

Hints

- Find each child’s total sleep time separately. - Use midnight as a point for splitting each time interval. - Compare each total with \(10\) hours.

Solution

1. Lucas sleeps \(3\) hours \(30\) minutes before midnight and \(7\) hours \(15\) minutes after midnight. His total is \(10\) hours \(45\) minutes, which is \(45\) minutes more than \(10\) hours. 2. Maria sleeps \(2\) hours \(45\) minutes before midnight and \(6\) hours \(45\) minutes after midnight. Her total is \(9\) hours \(30\) minutes, which is \(30\) minutes less than \(10\) hours.

Answer

Lucas sleeps \(45\) minutes longer than the comparison value. Maria sleeps \(30\) minutes less than the comparison value.
5182083
Mr. Smith works at a bakery and must arrive at \(3{:}15\,\text{a.m.}\). He wants exactly \(7\) hours \(30\) minutes of sleep. After waking up, he needs \(45\) minutes to get ready and drive to work. What is the latest time he can go to bed the night before?

Hints

- Combine the sleep time and the time needed after waking up. - Work backward from the required arrival time. - Use midnight as a point for splitting the calculation. - Make sure the answer is on the previous evening.

Solution

1. Find the total time needed before work: \(7\,\text{hours}\,30\,\text{minutes} + 45\,\text{minutes} = 8\,\text{hours}\,15\,\text{minutes}\). 2. Work backward from \(3{:}15\,\text{a.m.}\) by \(3\) hours \(15\) minutes to reach midnight. 3. The remaining time is \(8\,\text{hours}\,15\,\text{minutes} - 3\,\text{hours}\,15\,\text{minutes} = 5\,\text{hours}\). 4. Five hours before midnight is \(7{:}00\,\text{p.m.}\) the night before.

Answer

Mr. Smith must go to bed by \(7{:}00\,\text{p.m.}\) the night before.
5182133
Two trains travel the same route. Train A leaves at \(8{:}45\,\text{a.m.}\) and arrives at \(11{:}20\,\text{a.m.}\). Train B leaves at \(1{:}55\,\text{p.m.}\) and arrives at \(4{:}15\,\text{p.m.}\). Which train takes less time, and what is the difference in minutes?

Hints

- Find each train’s travel time separately. - Count to the next full hour, then count the remaining time. - Compare the two durations. - Express the difference in minutes.

Solution

1. Find Train A’s travel time: From \(8{:}45\,\text{a.m.}\) to \(11{:}20\,\text{a.m.}\) is \(2\) hours \(35\) minutes. 2. Find Train B’s travel time: From \(1{:}55\,\text{p.m.}\) to \(4{:}15\,\text{p.m.}\) is \(2\) hours \(20\) minutes. 3. Compare the times. Train B takes less time. 4. Find the difference: \(2\,\text{hours}\,35\,\text{minutes} - 2\,\text{hours}\,20\,\text{minutes} = 15\,\text{minutes}\).

Answer

Train B takes less time by \(15\) minutes.
5182193
An overnight train arrives at \(7{:}15\,\text{a.m.}\). The trip lasts \(8\) hours \(45\) minutes. What time did the train leave the previous evening?

Hints

- Find how much of the trip occurs after midnight. - Subtract that amount from the full trip time. - Count the remaining time backward from midnight.

Solution

1. From midnight to \(7{:}15\,\text{a.m.}\) is \(7\) hours \(15\) minutes. 2. Find the part of the trip before midnight: \(8\,\text{hours}\,45\,\text{minutes} - 7\,\text{hours}\,15\,\text{minutes} = 1\,\text{hour}\,30\,\text{minutes}\). 3. One hour \(30\) minutes before midnight is \(10{:}30\,\text{p.m.}\).

Answer

The train left at \(10{:}30\,\text{p.m.}\).
5182203
A chess tournament begins at \(1{:}30\,\text{p.m.}\). It has three rounds that each last \(45\) minutes. There is a \(15\)-minute break after the first round and another \(15\)-minute break after the second round. What time does the tournament end?

Hints

- How many breaks occur between three rounds? - Add the playing time and break time. - Convert the total minutes to hours and minutes. - Add the duration to the starting time.

Solution

1. Find the total playing time: \(3 \times 45 = 135\) minutes. 2. Find the total break time: \(2 \times 15 = 30\) minutes. 3. Find the total tournament time: \(135 + 30 = 165\) minutes, which is \(2\) hours \(45\) minutes. 4. Add the duration to the start: \(1{:}30\,\text{p.m.} + 2\,\text{hours}\,45\,\text{minutes} = 4{:}15\,\text{p.m.}\).

Answer

The tournament ends at \(4{:}15\,\text{p.m.}\).
5200453
An adventure camp lasts exactly \(100\) days. It begins on September 1, and September 1 is Day \(1\). a) In which month does the camp end? b) How many camp days occur in October? c) What is the date of the final camp day?

Hints

- Write the number of days in September, October, and November. - Add the month totals until you are close to \(100\). - Find how many days remain after November. - Those remaining days determine the ending date in December.

Solution

1. September has \(30\) days, October has \(31\) days, and November has \(30\) days. 2. Through the end of November, \(30 + 31 + 30 = 91\) camp days have passed. 3. Find the remaining days: \(100 - 91 = 9\). 4. Those \(9\) days occur in December, so Day \(100\) is December 9. 5. All \(31\) days of October are included in the camp.

Answer

a) The camp ends in December. b) \(31\) camp days occur in October. c) The final camp day is December 9.
5201293
A movie ends at \(4{:}10\) p.m. The movie itself lasts \(95\) minutes. Before it begins, advertisements play for exactly \(15\) minutes. At what time do the advertisements begin?

Hints

- Find the total length of the advertisements and the movie. - Count backward from the ending time. - Convert the total minutes to hours and minutes before counting back.

Solution

1. Find the total program length: \(95\,\text{min} + 15\,\text{min} = 110\,\text{min}\). 2. Convert the duration: \(110\,\text{min} = 1\) hour \(50\) minutes. 3. Count backward from \(4{:}10\) p.m. by \(1\) hour \(50\) minutes to get \(2{:}20\) p.m.

Answer

The advertisements begin at \(2{:}20\) p.m.
5201373
Lucas wants dinner to be ready at \(6{:}30\) p.m. Preparing the food takes \(25\) minutes, and baking it takes another \(45\) minutes. What is the latest time Lucas can begin preparing the food?

Hints

- Find the total preparation and baking time. - Work backward from the dinner time. - How many minutes are in \(1\) hour? - Express the total duration in hours and minutes.

Solution

1. Find the total time: \(25\,\text{min} + 45\,\text{min} = 70\,\text{min}\), or \(1\) hour \(10\) minutes. 2. Count backward from \(6{:}30\) p.m. by \(1\) hour to \(5{:}30\) p.m. 3. Count back another \(10\) minutes to \(5{:}20\) p.m.

Answer

Lucas must begin by \(5{:}20\) p.m.
5201493
Lucas has a \(45\)-minute piano lesson that ends at \(4{:}15\) p.m. It takes him exactly \(15\) minutes to travel from home to the music school. At what time must Lucas leave home to arrive when the lesson begins?

Hints

- Find the lesson's starting time by counting back from its ending time. - Work backward in steps. - Then subtract the travel time.

Solution

1. Count back \(45\) minutes from \(4{:}15\) p.m. The lesson begins at \(3{:}30\) p.m. 2. Count back the \(15\)-minute travel time: \(3{:}30\) p.m. minus \(15\) minutes is \(3{:}15\) p.m.

Answer

Lucas must leave home at \(3{:}15\) p.m.
5201523
A baker takes finished loaves out of the oven at \(11{:}15\) a.m. The loaves baked for exactly \(1\) hour \(50\) minutes. At what time did the baker put them in the oven?

Hints

- Count backward in steps. - Subtract the full hour first. - Then count back the remaining minutes. - A time line may help.

Solution

1. Count back \(1\) hour from \(11{:}15\) a.m. to \(10{:}15\) a.m. 2. Count back another \(50\) minutes: \(15\) minutes to \(10{:}00\) a.m. and \(35\) more minutes to \(9{:}25\) a.m.

Answer

The baker put the loaves in the oven at \(9{:}25\) a.m.
5206033
A cake bakes for exactly \(55\) minutes. It is taken out of the oven at \(2{:}10\) p.m. At what time was it put in the oven?

Hints

- Count backward from the ending time. - Split the baking time so you reach a whole hour first. - A clock drawing or time line may help.

Solution

1. Count backward \(10\) minutes from \(2{:}10\) p.m. to \(2{:}00\) p.m. 2. Of the \(55\) minutes, \(55 - 10 = 45\) minutes remain. 3. Count back \(45\) more minutes from \(2{:}00\) p.m. to \(1{:}15\) p.m.

Answer

The cake was put in the oven at \(1{:}15\) p.m.
5210033
Complete the missing times and durations in the TV schedule. <table> <tr> <td>Program</td> <td>Start</td> <td>End</td> <td>Duration</td> </tr> <tr> <td>Nature Wonders</td> <td>\(10{:}35\) a.m.</td> <td>\(11{:}20\) a.m.</td> <td></td> </tr> <tr> <td>Cartoons</td> <td></td> <td>\(1{:}15\) p.m.</td> <td>\(45\,\text{min}\)</td> </tr> <tr> <td>Sports</td> <td>\(2{:}50\) p.m.</td> <td></td> <td>\(2\,\text{hr}\,15\,\text{min}\)</td> </tr> <tr> <td>Late Movie</td> <td>\(10{:}45\) p.m.</td> <td>\(12{:}30\) a.m.</td> <td></td> </tr> </table>

Hints

- Count to the next hour first when that makes the elapsed time easier. - To find a start time, subtract the duration from the end time. - The Late Movie crosses midnight. How much time passes before and after midnight?

Solution

1. Nature Wonders runs from \(10{:}35\) a.m. to \(11{:}20\) a.m., which is \(45\) minutes. 2. Cartoons ends at \(1{:}15\) p.m. Subtract \(45\) minutes to get a start time of \(12{:}30\) p.m. 3. Sports starts at \(2{:}50\) p.m. Add \(2\) hours and \(15\) minutes to get an end time of \(5{:}05\) p.m. 4. The Late Movie runs \(1\) hour \(15\) minutes before midnight and \(30\) minutes after midnight, for a total of \(1\) hour \(45\) minutes.

Answer

Nature Wonders: \(45\,\text{min}\) Cartoons: starts at \(12{:}30\) p.m. Sports: ends at \(5{:}05\) p.m. Late Movie: \(1\,\text{hr}\,45\,\text{min}\)
5210043
Find the missing information for each commuter train trip. a) Train 1 leaves at \(7{:}42\) a.m. and arrives at \(9{:}15\) a.m. How long is the trip? b) Train 2 takes \(2\,\text{hr}\,8\,\text{min}\) and arrives at \(12{:}03\) p.m. What time did it leave? c) Train 3 leaves at \(11{:}18\) p.m. The trip takes \(1\,\text{hr}\,55\,\text{min}\). What time does it arrive?

Hints

- It can help to count to the next hour first. - For c), find how much time passes before midnight. - You can also convert each time span to minutes.

Solution

1. For a), the time from \(7{:}42\) a.m. to \(8{:}00\) a.m. is \(18\) minutes, and the time from \(8{:}00\) a.m. to \(9{:}15\) a.m. is \(1\) hour \(15\) minutes. The total is \(1\) hour \(33\) minutes. 2. For b), subtract \(2\) hours from \(12{:}03\) p.m. to get \(10{:}03\) a.m. Then subtract \(8\) minutes to get \(9{:}55\) a.m. 3. For c), add \(42\) minutes to reach midnight, leaving \(1\) hour \(13\) minutes. Adding that remaining time gives \(1{:}13\) a.m.

Answer

a) \(1\,\text{hr}\,33\,\text{min}\) b) \(9{:}55\) a.m. c) \(1{:}13\) a.m.
5210203
A hiking group starts a trip at \(8{:}35\) a.m. and reaches its destination at \(2{:}15\) p.m. The group takes two breaks: one from \(10{:}20\) a.m. to \(10{:}55\) a.m. and another from \(12{:}30\) p.m. to \(1{:}05\) p.m. How long was the group moving?

Hints

- First find the total time from departure to arrival. - Find the length of each break. - Subtract all break time from the total trip time. - Remember that \(60\) minutes make one hour.

Solution

1. The total trip time from \(8{:}35\) a.m. to \(2{:}15\) p.m. is \(5\) hours \(40\) minutes. 2. The first break lasts \(35\) minutes, and the second break also lasts \(35\) minutes. 3. The total break time is \(35 + 35 = 70\) minutes, or \(1\) hour \(10\) minutes. 4. Subtract the breaks: \(5\,\text{hr}\,40\,\text{min} - 1\,\text{hr}\,10\,\text{min} = 4\,\text{hr}\,30\,\text{min}\).

Answer

The group was moving for \(4\,\text{hr}\,30\,\text{min}\).
5210213
Lena compares two workout times. On Monday, she works out from \(4{:}15\) p.m. to \(6{:}40\) p.m. and takes a \(20\)-minute break. On Wednesday, she works out from \(3{:}50\) p.m. to \(6{:}10\) p.m. without a break. On which day is her actual workout time longer? Find the difference in minutes.

Hints

- Find the actual workout time for each day separately. - Subtract Monday's break. - Convert both times to minutes before comparing. - Subtract the shorter time from the longer time.

Solution

1. Monday's total time is \(2\) hours \(25\) minutes. After subtracting the \(20\)-minute break, the actual workout time is \(2\) hours \(5\) minutes, or \(125\) minutes. 2. Wednesday's workout lasts \(2\) hours \(20\) minutes, or \(140\) minutes. 3. Since \(140 > 125\), Wednesday's workout is longer. 4. The difference is \(140 - 125 = 15\) minutes.

Answer

Her actual workout time is longer on Wednesday by \(15\) minutes.
5210403
Compare the daylight on two days. - Day A: sunrise at \(5{:}28\) a.m. and sunset at \(8{:}45\) p.m. - Day B: sunrise at \(7{:}52\) a.m. and sunset at \(4{:}15\) p.m. How much longer is the daylight on Day A? Give the difference in hours and minutes.

Hints

- Find the daylight duration for each day first. - Find each elapsed time from sunrise to sunset. - When subtracting durations, you can regroup one hour as \(60\) minutes. - Subtract the shorter daylight duration from the longer one.

Solution

1. Day A has \(15\) hours \(17\) minutes of daylight. 2. Day B has \(8\) hours \(23\) minutes of daylight. 3. Subtract the two durations. Regroup \(15\) hours \(17\) minutes as \(14\) hours \(77\) minutes. 4. Then \(14\,\text{hr}\,77\,\text{min} - 8\,\text{hr}\,23\,\text{min} = 6\,\text{hr}\,54\,\text{min}\).

Answer

Day A has \(6\,\text{hr}\,54\,\text{min}\) more daylight than Day B.
5210413
A film crew wants to record outdoors during daylight on two days. - On Day 1, the sun rises at \(6{:}15\) a.m. and sets at \(7{:}27\) p.m. - On Day 2, the sun rises at \(7{:}05\) a.m. and sets at \(6{:}50\) p.m. How much daylight is available altogether? Give the total in days, hours, and minutes.

Hints

- Find the daylight duration for each day separately. - Add the two durations. - How many hours make one full day?

Solution

1. Day 1 has \(13\) hours \(12\) minutes of daylight. 2. Day 2 has \(11\) hours \(45\) minutes of daylight. 3. Add the two durations: \(13\,\text{hr}\,12\,\text{min} + 11\,\text{hr}\,45\,\text{min} = 24\,\text{hr}\,57\,\text{min}\). 4. Since \(24\) hours equals \(1\) day, the total is \(1\) day, \(0\) hours, and \(57\) minutes.

Answer

The crew has \(1\) day, \(0\) hours, and \(57\) minutes of daylight altogether, which is \(24\,\text{hr}\,57\,\text{min}\).
5210483
The table shows three train trips from Central Station to Riverside Station. <table> <tr> <td>Train</td> <td>Leaves Central Station</td> <td>Intermediate stop</td> <td>Arrives at Riverside Station</td> </tr> <tr> <td>Express 173</td> <td>\(8{:}26\) a.m.</td> <td>Lakeview at \(10{:}18\) a.m.</td> <td>\(10{:}25\) a.m.</td> </tr> <tr> <td>Regional 24</td> <td>\(8{:}55\) a.m.</td> <td>Cedar Junction at \(10{:}20\) a.m.</td> <td>\(11{:}45\) a.m.</td> </tr> <tr> <td>Express 1591</td> <td>\(9{:}16\) a.m.</td> <td>None</td> <td>\(11{:}07\) a.m.</td> </tr> </table> a) Which trip has the shortest travel time from Central Station to Riverside Station, and how long is it? b) How long does Regional 24 take from Cedar Junction to Riverside Station?

Hints

- Find the elapsed time from each departure at Central Station to its arrival at Riverside Station. - Work with the hours and minutes carefully. - For b), use only the two times listed in the Regional 24 row.

Solution

1. Express 173 takes \(1\) hour \(59\) minutes, from \(8{:}26\) a.m. to \(10{:}25\) a.m. 2. Regional 24 takes \(2\) hours \(50\) minutes, from \(8{:}55\) a.m. to \(11{:}45\) a.m. 3. Express 1591 takes \(1\) hour \(51\) minutes, from \(9{:}16\) a.m. to \(11{:}07\) a.m. This is the shortest trip. 4. Regional 24 travels from Cedar Junction at \(10{:}20\) a.m. to Riverside Station at \(11{:}45\) a.m., a time of \(1\) hour \(25\) minutes.

Answer

a) Express 1591; \(1\,\text{hr}\,51\,\text{min}\) b) \(1\,\text{hr}\,25\,\text{min}\)
5212493
Liam plans to practice basketball for exactly \(12\) hours this week. His times from Monday through Thursday are shown below. <table> <tr> <th>Day</th> <th>Start</th> <th>End</th> </tr> <tr> <td>Monday</td> <td>\(4{:}15\) p.m.</td> <td>\(6{:}45\) p.m.</td> </tr> <tr> <td>Tuesday</td> <td>\(5{:}00\) p.m.</td> <td>\(7{:}15\) p.m.</td> </tr> <tr> <td>Wednesday</td> <td>\(3{:}45\) p.m.</td> <td>\(6{:}30\) p.m.</td> </tr> <tr> <td>Thursday</td> <td>\(4{:}30\) p.m.</td> <td>\(7{:}00\) p.m.</td> </tr> </table> On Friday, Liam starts at \(3{:}30\) p.m. What time must he finish to reach exactly \(12\) hours?

Hints

- Find the practice time for each day. - Add the four durations. - How much time remains to reach \(12\) hours? - Add that remaining time to Friday's start time.

Solution

1. The daily practice times are \(2\) hours \(30\) minutes, \(2\) hours \(15\) minutes, \(2\) hours \(45\) minutes, and \(2\) hours \(30\) minutes. 2. The total from Monday through Thursday is \(10\) hours. 3. Liam needs \(12 - 10 = 2\) more hours. 4. Two hours after \(3{:}30\) p.m. is \(5{:}30\) p.m.

Answer

Liam must finish at \(5{:}30\) p.m.
5213633
An express train leaves Harbor City at \(9{:}12\) a.m. and arrives in Pine Valley at \(10{:}05\) a.m. The train stops there for \(4\) minutes. The trip from Pine Valley to Summit City then takes \(58\) minutes. a) How long is the trip from Harbor City to Pine Valley? b) What time does the train arrive in Summit City? c) A passenger claims, “The total time from leaving Harbor City to arriving in Summit City is exactly two hours.” Is the claim correct? Show why.

Hints

- Count to the next hour first for part a). - Include the station stop before adding the second travel time. - Compare the total elapsed time with \(120\) minutes.

Solution

1. The trip from \(9{:}12\) a.m. to \(10{:}05\) a.m. takes \(53\) minutes. 2. After the \(4\)-minute stop, the train leaves Pine Valley at \(10{:}09\) a.m. 3. Adding \(58\) minutes gives an arrival time of \(11{:}07\) a.m. 4. The total elapsed time from \(9{:}12\) a.m. to \(11{:}07\) a.m. is \(1\) hour \(55\) minutes, or \(115\) minutes. This is \(5\) minutes less than two hours.

Answer

a) \(53\,\text{min}\) b) \(11{:}07\) a.m. c) No. The total time is \(1\,\text{hr}\,55\,\text{min}\), not \(2\) hours.
5217843
A bicycle group starts at the town square at \(10{:}15\) a.m. It rides \(45\) minutes to a lookout point, stops there for \(1\,\text{hr}\,15\,\text{min}\), rides \(35\) minutes to a park cafe, stops for lunch for \(40\) minutes, and then rides \(55\) minutes back to the town square. What time does the group return?

Hints

- Add each travel time and stop time in order. - Count to the next hour when that helps. - Remember that \(60\) minutes make one hour. - A small timeline or table may help organize the events.

Solution

1. After the first \(45\)-minute ride, the group arrives at \(11{:}00\) a.m. 2. After the \(1\)-hour \(15\)-minute stop, it leaves at \(12{:}15\) p.m. 3. After riding \(35\) minutes, it arrives at the cafe at \(12{:}50\) p.m. 4. After the \(40\)-minute lunch, it leaves at \(1{:}30\) p.m. 5. After the \(55\)-minute return ride, it arrives at \(2{:}25\) p.m.

Answer

The bicycle group returns at \(2{:}25\) p.m.
5217853
A hiking group is following a loop trail. The section from point A to point B is \(3\,\text{mi}\) and takes \(65\) minutes. The group then hikes \(2\,\text{mi}\) from point B to point C in \(45\) minutes. At point C, the group takes a \(30\)-minute break. The entire loop from A to B to C and back to A is \(8\,\text{mi}\). The final section from C to A takes \(70\) minutes. a) How long is the section from point C back to point A? b) The group starts at \(8{:}30\) a.m. What time does it return to point A?

Hints

- Subtract the first two sections from the total trail length. - Add the hiking times and the break time. - Regroup every \(60\) minutes as one hour.

Solution

1. Subtract the two known trail sections from the total distance: \(8\,\text{mi}-3\,\text{mi}-2\,\text{mi}=3\,\text{mi}\). 2. Add all hiking and break times: \(65+45+30+70=210\) minutes. 3. Since \(210\) minutes is \(3\) hours \(30\) minutes, add that elapsed time to \(8{:}30\) a.m. The group returns at \(12{:}00\) p.m.

Answer

a) The section from C to A is \(3\,\text{mi}\). b) The group returns at \(12{:}00\) p.m.
5217863
Lucas and Maria meet at a lookout tower. Lucas leaves home at \(2{:}15\) p.m. and takes \(50\) minutes to get there. Maria leaves later, takes only \(30\) minutes, and arrives at the same time as Lucas. They stay at the tower for \(20\) minutes. Then they travel together to Lucas's home. The return trip takes \(10\) minutes less than Lucas's trip to the tower. a) What time did Maria leave home? b) What time do they arrive at Lucas's home?

Hints

- First find when Lucas reaches the tower. - Maria arrives at the same time, so work backward from that time. - Find the return-trip duration before adding it. - Include the time spent at the tower.

Solution

1. Lucas arrives at the tower at \(2{:}15\) p.m. plus \(50\) minutes, or \(3{:}05\) p.m. 2. Maria also arrives at \(3{:}05\) p.m. Subtracting her \(30\)-minute travel time gives a start time of \(2{:}35\) p.m. 3. They leave the tower \(20\) minutes later, at \(3{:}25\) p.m. 4. The return trip takes \(50 - 10 = 40\) minutes. 5. They arrive at Lucas's home at \(3{:}25\) p.m. plus \(40\) minutes, or \(4{:}05\) p.m.

Answer

a) \(2{:}35\) p.m. b) \(4{:}05\) p.m.
5313533
A cake must bake for exactly \(45\) minutes. Ms. Miller takes the finished cake out of the oven at \(4{:}10\) p.m. What time did she put it in the oven?

Hints

- You are looking for the start time, so count backward from the ending time. - Use the hour as a helpful stopping point.

Solution

1. Count back \(10\) minutes from \(4{:}10\) p.m. to \(4{:}00\) p.m. 2. There are \(45 - 10 = 35\) minutes left to count back. 3. Count back \(35\) minutes from \(4{:}00\) p.m. The cake went into the oven at \(3{:}25\) p.m.

Answer

She put the cake in the oven at \(3{:}25\) p.m.
5313613
Two trains travel the same route. Train A leaves at \(7{:}45\,\text{a.m.}\) and arrives at \(9{:}12\,\text{a.m.}\) Train B leaves at \(8{:}20\,\text{a.m.}\) and arrives at \(9{:}55\,\text{a.m.}\) Which train has the shorter travel time, and what is the difference in minutes?

Hints

- Find each train's travel time separately. - Convert both travel times to minutes before comparing them. - Subtract the shorter time from the longer time.

Solution

1. Train A travels from \(7{:}45\,\text{a.m.}\) to \(9{:}12\,\text{a.m.}\), which is \(1\) hour \(27\) minutes, or \(87\) minutes. 2. Train B travels from \(8{:}20\,\text{a.m.}\) to \(9{:}55\,\text{a.m.}\), which is \(1\) hour \(35\) minutes, or \(95\) minutes. 3. Since \(87 < 95\), Train A has the shorter travel time. 4. The difference is \(95 - 87 = 8\) minutes.

Answer

Train A has the shorter travel time by \(8\) minutes.
5314333
Anna and Ben spent Saturday at a swimming pool. Clocks a) and c) show when Anna arrived and left. Clocks b) and d) show when Ben arrived and left. Who spent more time at the pool?
Figure for problem 531433

Hints

- Use clocks a) and c) for Anna and clocks b) and d) for Ben. - Find each person's elapsed time separately. - Compare the two elapsed times.

Solution

1. Anna arrived at \(10{:}15\,\text{a.m.}\) and left at \(2{:}30\,\text{p.m.}\) Her time at the pool was \(4\) hours \(15\) minutes. 2. Ben arrived at \(11{:}05\,\text{a.m.}\) and left at \(3{:}30\,\text{p.m.}\) His time at the pool was \(4\) hours \(25\) minutes. 3. Since \(4\,\text{hours}\,25\,\text{minutes} > 4\,\text{hours}\,15\,\text{minutes}\), Ben spent more time at the pool.

Answer

Ben spent more time at the pool. Anna stayed \(4\) hours \(15\) minutes, and Ben stayed \(4\) hours \(25\) minutes.
5314363
Lucas reads a book in the afternoon. Clock a) shows when he starts, and clock b) shows when he stops. During that time, he takes a \(15\)-minute break. How long does Lucas actually spend reading? Give your answer in hours and minutes.
Figure for problem 531436

Hints

- Read the two clock times and remember that both are in the afternoon. - Find the total elapsed time from clock a) to clock b). - Subtract the break from the total time.

Solution

1. Clock a) shows \(3{:}10\,\text{p.m.}\), and clock b) shows \(4{:}45\,\text{p.m.}\) 2. The elapsed time from \(3{:}10\,\text{p.m.}\) to \(4{:}45\,\text{p.m.}\) is \(1\) hour \(35\) minutes, or \(95\) minutes. 3. Subtract the break: \(95 - 15 = 80\) minutes. 4. Convert \(80\) minutes to \(1\) hour \(20\) minutes.

Answer

Lucas spends \(1\) hour \(20\) minutes reading.

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