An elephant herd travels \(20\) miles in a day while moving at \(4\) miles per hour. How many hours does the herd travel?

A delivery van travels at a constant rate shown in the table. <table> <tr><th>Time (hours)</th><th>Distance (miles)</th></tr> <tr><td>\(2\)</td><td>\(90\)</td></tr> <tr><td>\(5\)</td><td>\(225\)</td></tr> </table> What is the unit rate, and what does it mean in this situation?

A cyclist travels \(18\) miles in \(3\) hours at a steady speed. How far does the cyclist travel in one hour?

A popcorn stand makes \(8\) bags of popcorn every minute at a steady rate. a) What does “\(8\) bags per minute” tell you? b) How many bags can it make in \(3\) minutes?

Four passes to a swimming pool cost \(\$14\). Each pass has the same price. How much does one pass cost? Explain what the unit price means.

A print shop's printer works at a steady rate. Fill in the missing number of pages and explain your method. <table><tr><th>Minutes</th><th>Pages printed</th></tr><tr><td>\(1\)</td><td>\(5\)</td></tr><tr><td>\(8\)</td><td>\(\square\)</td></tr></table>

How many miles does the hiker travel in one hour at the steady pace shown? Explain using a point on the graph.

A student wraps one gift in \(3\) minutes. The student keeps the same pace. How many minutes will it take to wrap \(5\) gifts? Explain which quantity is measured “per gift.”

At a farmers market, organic tomatoes cost \(\$4.80\) per pound. Mrs. Miller buys exactly \(2.25\) lb of tomatoes. What is the total cost?

Two cyclists compare training distances. Rider A completes \(14.5\) laps of a course that is \(2.25\) miles long. Rider B says, “I rode \(33\) miles today, so I went farther than you.” Use a calculation to determine whether Rider B is correct.

A grocery store has two orange specials. Deal A: \(15\) oranges for \(\$5.85\) Deal B: \(12\) oranges for \(\$4.80\) Which deal has the lower price per orange? Find both unit prices.

A class is making fruit punch for a school event. A recipe uses \(2.5\) gallons of juice for \(25\) people. How much juice is needed for \(60\) people? Write an equation to solve the problem.

A grocery store sells the same pasta in two package sizes. Package A contains \(12\,\text{oz}\) and costs \(\$1.80\). Package B contains \(20\,\text{oz}\) and costs \(\$2.80\). Find the price per ounce for each package. Which package is the better buy, and what is the difference in price per ounce?

A pancake recipe for \(4\) people uses \(2\) cups of flour and \(3\) eggs. a) How many cups of flour are needed for \(10\) people? b) If \(15\) eggs are used and all other ingredients are adjusted in the same ratio, how many people will the recipe serve?

A juice bar sells fresh juice in three cup sizes: - Small: \(8\,\text{fl oz}\) for \(\$2.20\) - Medium: \(12\,\text{fl oz}\) for \(\$3.00\) - Large: \(20\,\text{fl oz}\) for \(\$4.50\) a) Find the price per \(4\,\text{fl oz}\) for each cup size. b) Which cup size has the lowest price per \(4\,\text{fl oz}\)? c) If juice could be bought at that same rate, how much would \(36\,\text{fl oz}\) cost?

A clock’s minute hand moves at a constant rate. Find how many minutes pass while the hand sweeps through each angle. a) \(48^\circ\) b) \(162^\circ\) c) \(210^\circ\) d) \(540^\circ\)

A garden hose delivers water at a constant rate of \(12\,\text{gal/min}\). How long will it take to fill a small pool that holds \(1500\,\text{gal}\)? Give your answer in hours and minutes.

A delivery driver travels at a constant rate of \(50\) miles per hour. Complete the table. <table> <tr> <td>Time</td> <td>\(1\,\text{h}\)</td> <td>\(2\,\text{h}\)</td> <td>\(4\,\text{h}\)</td> <td>\(10\,\text{h}\)</td> <td>\(\frac{1}{2}\,\text{h}\)</td> </tr> <tr> <td>Distance</td> <td>\(50\,\text{mi}\)</td> <td>?</td> <td>?</td> <td>?</td> <td>?</td> </tr> </table>

A hiker walks at a constant rate of \(4\) miles per hour. a) How far does the hiker walk in \(3\) hours? b) How far does the hiker walk in half an hour? c) How many hours does it take the hiker to walk \(24\) miles?

A parking garage charges by the minute at a rate of \(\$4\) per hour. Complete the table. <table> <tr> <td>Parking time</td> <td>\(1\,\text{hr}\)</td> <td>\(2\,\text{hr}\)</td> <td>\(30\,\text{min}\)</td> <td>\(1\,\text{hr}\ 30\,\text{min}\)</td> <td>\(3\,\text{hr}\)</td> </tr> <tr> <td>Cost</td> <td>\(\$4\)</td> <td></td> <td></td> <td></td> <td></td> </tr> </table>

Renting an electric bicycle costs \(\$12\) per hour. The shop also charges for parts of an hour at the same rate. Find each rental price. <table><tr><th>Rental time</th><td>\(30\,\text{min}\)</td><td>\(15\,\text{min}\)</td><td>\(45\,\text{min}\)</td><td>\(2\,\text{h}\ 15\,\text{min}\)</td><td>\(3\,\text{h}\ 30\,\text{min}\)</td></tr><tr><th>Price</th><td>\(\square\)</td><td>\(\square\)</td><td>\(\square\)</td><td>\(\square\)</td><td>\(\square\)</td></tr></table>

A gardener works in a park from \(8{:}30\) a.m. to \(11{:}30\) a.m. The gardener charges \(\$42\) per hour. What is the total charge?

An IT technician works in an office from \(2{:}15\) p.m. to \(4{:}45\) p.m. The rate is \(\$64\) per hour. How much must the office pay?

A campground charges \(\$12\) per night for a small tent site. a) Complete the price table. <table> <tr><th>Nights</th><td>\(1\)</td><td>\(2\)</td><td>\(3\)</td><td>\(5\)</td><td>\(8\)</td><td>\(10\)</td></tr> <tr><th>Price</th><td>\(\$12\)</td><td></td><td></td><td></td><td></td><td></td></tr> </table> b) What is the total price for \(14\) nights?

At an ice cream shop, each scoop costs the same amount, with no discounts for larger orders. Four scoops cost \(\$6.00\). a) How much do \(8\) scoops cost? b) How much do \(2\) scoops cost?

An amusement park has two kinds of boats for a canal ride. Wave: total weight limit \(560\,\text{kg}\), with \(8\) seats. Anchor: total weight limit \(450\,\text{kg}\), with \(6\) seats. What is the average share of the total weight limit per seat for each boat? Which boat has the larger share? This is not a weight limit for an individual rider.

An orchard produces \(48{,}000\,\text{L}\) of apple juice in a year. On average, one mature apple tree provides enough apples for about \(60\,\text{L}\) of juice. About how many apple trees are needed to produce that amount?

A region uses about \(900{,}000\,\text{L}\) of milk each month. A tanker truck carries \(15{,}000\,\text{L}\) per full load. About how many full truckloads equal the monthly amount?

A large aquarium holds \(200\) gallons of water. Water costs \(\$5.00\) per \(1000\) gallons. a) What does it cost to fill the aquarium completely? b) Once a month, half of the water is replaced for cleaning. What does one water change cost?

A packing machine fills \(12\) bags of apples in \(3\) minutes. At the same constant rate, how many bags does it fill in \(10\) minutes?

A baker uses \(35\,\text{lb}\) of flour in \(5\) days. He bakes the same amount of bread each day. a) How many pounds of flour does he use each day? b) How many days will a \(56\,\text{lb}\) supply last if he continues using flour at the same daily rate?

A bakery machine packs \(40\) bags of dinner rolls in \(5\) minutes. At the same constant rate, how many bags does it pack in \(15\) minutes?

A warehouse divides \(72\,\text{L}\) of apple juice equally among \(6\) large containers. A delivery requires \(156\,\text{L}\) of juice. How many containers of the same size are needed?

A fruit salad recipe uses \(1.5\,\text{lb}\) of apples for \(4\) people. A class wants to make enough fruit salad for \(20\) people. How many pounds of apples are needed?

A truck delivers \(48\) tons of sand in \(6\) full loads. At the same rate, how many loads are needed to deliver \(72\) tons?

Four apples have a total weight of \(1.25\,\text{lb}\). How many of these apples are in a bag weighing \(5\,\text{lb}\)?

A hot-air balloon takes off when the ground temperature is \(7\,^{\circ}\text{C}\). In a simplified model, the temperature drops by \(1\,^{\circ}\text{C}\) for every \(100\,\text{m}\) the balloon rises. The balloon rises \(1800\,\text{m}\). What temperature does the model predict?

A package of \(5\) markers costs \(\$4.50\). A value pack of \(12\) markers costs \(\$9.60\). How many cents less does each marker cost in the value pack?

A recycling process turns \(12\,\text{kg}\) of used paper into \(9\,\text{kg}\) of new paper. A school collects \(480\,\text{kg}\) of used paper. How many kilograms of new paper can be produced at the same rate?

A movie theater concession stand sells popcorn at a constant rate of \(5\) bags per minute. How many bags are sold in half an hour?

When a freezer is turned on, its internal temperature decreases from \(18\,^{\circ}\text{C}\) to \(-12\,^{\circ}\text{C}\). The temperature decreases at a constant rate of \(5\,^{\circ}\text{C}\) per hour. How many hours does the cooling process take?

A sports shop sells tennis balls individually at the same price per ball. Four balls cost \(\$6.40\). a) How much do \(8\) balls cost? b) How much does \(1\) ball cost? c) How much do \(15\) balls cost?

A recipe for \(4\) servings of rice pudding uses exactly \(1\,\text{qt}\) of milk. How much milk is needed for \(20\) servings?

A package of \(500\) sheets of copier paper weighs \(5\,\text{lb}\). How much do \(100\) sheets of the same paper weigh?

A school copier prints \(30\) pages in \(2\) minutes at a constant rate. a) How many pages does it print in \(7\) minutes? b) How long does it take to print \(225\) pages?

At a farmers market, \(4\,\text{lb}\) of apples cost \(\$6.00\). a) How much do \(7\,\text{lb}\) of apples cost? b) How many pounds of apples can a customer buy for \(\$12.00\)?

Eighteen students order pizza for a class party. Their order costs \(\$108\). Four more students join, and the class orders extra pizza at the same cost per student. How much does the extra pizza cost?

A recycling process uses \(20\,\text{kg}\) of used paper to make \(16\,\text{kg}\) of new paper. How many kilograms of used paper are needed to make \(80\,\text{kg}\) of new paper at the same rate?

A cyclist travels \(9\,\text{km}\) in one-half hour. On average, how many meters does the cyclist travel per minute?

Three apples cost \(90\) cents. How much do \(6\) apples cost?

A cyclist travels \(s\) miles in \(t\) hours. a) Write an expression for the cyclist's average speed \(v\), in miles per hour. b) Find \(v\) for each set of values: 1) \(s=52.5\) miles and \(t=2.5\) hours 2) \(s=18.9\) miles and \(t=1.5\) hours

A customer buys \(6\) apples for a total of \(\$4.50\). 1) Find the price of one apple. 2) Write a formula for the total cost \(G\) of \(n\) apples at \(p\) dollars per apple. 3) Use the formula to find each total cost: a) \(15\) apples at \(\$0.60\) each b) \(8\) apples at \(\$1.10\) each

A mobile phone plan charges \(\$0.05\) per megabyte \((\text{MB})\) of data used while traveling abroad. Find the cost for each amount of data: a) \(10\,\text{MB}\) b) \(100\,\text{MB}\) c) \(250\,\text{MB}\) d) \(1.5\,\text{GB}\), using \(1\,\text{GB}=1000\,\text{MB}\) e) Write an expression for the cost of using \(m\,\text{MB}\).

The two aligned number lines show a bus traveling at a constant rate. Panel a) shows time in minutes, and panel b) shows distance in miles. How far has the bus traveled after \(4\) minutes?

The aligned number lines show a cyclist’s constant rate. Panel a) shows time in minutes, and panel b) shows distance in kilometers. The cyclist’s route is \(4500\,\text{m}\) long. Use the number-line relationship to determine how many minutes the route takes. Include the needed unit conversion.

A bakery packs \(24\) muffins equally into \(4\) trays. Ari divides \(4\div24\) and calls the result muffins per tray. What rate does Ari's calculation actually find? Give the correct rate in muffins per tray.

Three movie tickets cost \(\$21\). Tickets all have the same price. Complete the table. <table><tr><th>Tickets</th><td>\(3\)</td><td>\(1\)</td><td>\(5\)</td></tr><tr><th>Cost</th><td>\(\$21\)</td><td>\(\square\)</td><td>\(\square\)</td></tr></table>

The graph shows the distance a jogger travels at a steady pace. Use a plotted point after more than one hour to find the speed in miles per hour. Show your calculation.

A hose fills \(20\) gallons in \(4\) minutes at a steady rate. Find both its rate in gallons per minute and the time needed for one gallon in minutes per gallon. Explain why the two numbers have different units.

A ferry travels at \(8\,\text{mi/h}\). How many hours does it take to travel \(32\) miles at that speed?

Panel a) measures hours, and panel b) measures miles on the same trip. Each colored band shows one total time or distance. What is the travel speed in miles per hour?

A bookstore sells \(4\) notebooks for \(\$10\). Another store sells \(6\) of the same notebooks for \(\$13.50\). Which store has the lower price per notebook?

Juice bottles are sold only in packs of \(6\). Each pack costs \(\$12\). A team needs at least \(9\) bottles. How many whole packs must it buy, and how much will they cost?

A bike shop charges \(\$3\) to start a rental and \(\$2\) for each full hour. a) What does a one-hour rental cost? What does a two-hour rental cost? b) Ken says two hours must cost twice as much as one hour. Explain whether that works here.

A team mixes apple juice and sparkling water in the same ratio in two containers. A pitcher holds \(1.5\,\text{L}\), and a dispenser holds \(6\,\text{L}\). The pitcher contains \(600\,\text{mL}\) of apple juice. How much apple juice is in the dispenser? Justify your answer using equivalent ratios.

A bag of coffee beans is worth \(\$144\). After \(3\,\text{lb}\) of beans are removed, the remaining beans are worth \(\$108\). Assume the price per pound is constant. a) What was the original weight of the full bag? b) What would the full bag cost if the price were reduced by \(\$2\) per pound?

A car averages \(25\) miles per gallon. a) How many gallons of gas does it use to travel \(15\) miles? b) How far can it travel with \(21.25\) gallons of gas, assuming the same average fuel economy?

Luke rides his bike \(5.4\) miles in \(15\) minutes. His friend Sarah rides \(4.5\) miles in \(12\) minutes. a) Who has the greater average speed? Compare their speeds in miles per hour. b) At Sarah's speed, how many feet does she travel in one second? Use \(1\,\text{mile}=5280\,\text{ft}\) and \(1\,\text{hour}=3600\,\text{s}\).

In a drone race, Drone Alpha travels \(45.5\,\text{m}\) in \(3.5\,\text{s}\). Drone Beta travels \(61.2\,\text{m}\) in \(4.8\,\text{s}\). a) Find each drone's speed in meters per second. Which drone is faster? b) How many centimeters does the faster drone travel in \(0.01\) second?

Two garden hoses are tested while filling a small pool. Hose A delivers \(25.5\) gallons in \(1.5\) minutes. Hose B delivers \(32.4\) gallons in \(1.8\) minutes. a) Which hose has the greater flow rate in gallons per minute? b) How many gallons does the faster-flowing hose deliver in one second?

A large water tank can hold \(450\,\text{m}^3\) of water. Use \(1\,\text{m}^3=1000\,\text{L}\). a) Convert this volume to liters. b) A pump removes water at a rate of \(1500\,\text{L}\) per minute. How many hours will it take to empty the full tank?

An empty swimming pool is \(10\,\text{m}\) long and \(5\,\text{m}\) wide. A hose adds water at a constant rate of \(40\,\text{L}\) per minute. Use \(1\,\text{m}^3=1000\,\text{L}\). a) When the water reaches a depth of \(1.6\,\text{m}\), how many liters will the pool contain? b) How many hours and minutes will it take to reach that depth?

Two weather models predict how air temperature changes with altitude. Model A predicts a decrease of \(3.5^\circ\text{F}\) for every \(1000\,\text{ft}\) of altitude. Model B predicts a decrease of \(5.5^\circ\text{F}\) for every \(1000\,\text{ft}\). At sea level, the temperature is \(59^\circ\text{F}\). At an altitude of \(10{,}000\,\text{ft}\), what is the difference between the temperatures predicted by the two models? Before calculating, explain which model predicts the lower temperature.

Aoife wrote the following expression to model a temperature change during a mountain hike: \(50-\frac{9000-3000}{1000}\times3.5\) a) Evaluate the expression step by step. b) Describe a situation that this expression could represent. Explain what \(50\), \(3000\), \(9000\), and \(3.5\) mean in your situation.

A hiking trail is \(2.5\) miles long. Use \(1\,\text{mile}=5280\,\text{ft}\). a) Leon's average step length is \(2.2\,\text{ft}\). About how many steps does he take to cover the whole trail? b) His younger sister takes \(2000\) more steps on the same trail. What is her average step length in feet?

A town of \(80{,}000\) people collects \(2400\) metric tons of food scraps for compost each year. Use \(1\) metric ton \(=1000\,\text{kg}\). a) How many kilograms of food scraps does the town collect per person each year? b) Another town has \(120{,}000\) people. How many metric tons would it collect each year at the same per-person rate?

A snail travels an average of \(0.14\,\text{m}\) each minute. a) How far does it travel in \(7.5\) minutes? b) A second snail moves \(1.3\) times as fast as the first. How far does the second snail travel in \(7.5\) minutes?

A leaky faucet wastes \(0.045\) gallons of water per minute. How many gallons are wasted if the faucet leaks continuously for \(4.5\) hours?

A swimmer completes \(400\,\text{m}\) in \(4\) minutes \(24.8\) seconds. The pool is \(50\,\text{m}\) long. What was the swimmer's average time, in seconds, for one length of the pool?

A bottling machine fills \(112.5\) gallons of juice in \(15\) minutes. a) How many gallons does it fill per minute on average? b) How many seconds does it take, on average, to fill one gallon?

A peregrine falcon dives at \(324\,\text{km/h}\). A swift travels \(336\,\text{m}\) in \(12\) seconds. Use \(1\,\text{m/s}=3.6\,\text{km/h}\). a) Find the swift's speed in meters per second. b) Which bird has the greater speed? Convert the swift's speed to kilometers per hour before comparing.

A remote-controlled car travels \(188\,\text{m}\) in \(40\) seconds. A second model has a constant speed of \(16.2\,\text{km/h}\). Use \(1\,\text{m/s}=3.6\,\text{km/h}\). a) Find the first car's speed in meters per second. b) Which car is faster? Convert the first car's speed to kilometers per hour before comparing.

A car uses \(12\) gallons of gas to travel \(300\) miles. a) Find the average fuel used per mile, in gallons per mile. b) How many miles can the car travel on \(6\) gallons if the rate stays the same?

A school-supply store sells notebooks in two package sizes: Package A: \(8\) notebooks for \(\$6.40\). Package B: \(12\) notebooks for \(\$9.00\). a) Which package has the lower price per notebook? b) Suppose the store also sells notebooks individually at that lower unit price. How much would \(20\) notebooks cost?

A car uses \(6\) gallons of gasoline to travel \(150\) miles. Its fuel tank holds \(15\) gallons and is currently \(40\%\) full. Is there enough gasoline for a planned \(140\)-mile trip? Justify your answer with calculations.

In a school cafeteria, every serving of pasta costs the same amount. Three servings cost \(\$13.50\). a) Find the cost of \(5\) servings. b) How many servings can be purchased for \(\$31.50\)? c) Is the relationship between number of servings and total price proportional or not proportional? Justify your answer.

Consider the hour hand of an analog clock. a) What angle does the hour hand sweep through in exactly one hour? b) What angle does it sweep through in \(15\) minutes? c) Through how many degrees does the hour hand turn from \(8{:}00\) a.m. to \(11{:}30\) a.m.?

A scooter uses \(1.5\) gallons of gasoline for every \(60\) miles traveled. Gas costs \(\$3.60\) per gallon. Tim plans to ride to a concert \(27\) miles away and then ride home. a) How many gallons of gasoline will the round trip use? b) What will the gasoline cost for the trip?

A scooter has a \(2\)-gallon fuel tank. At current prices, a full tank costs \(\$7.20\). The scooter uses an average of \(1.2\) gallons for every \(60\) miles. a) Find the price of one gallon of gasoline. b) How far can the scooter travel on a full tank, in theory? c) A day trip is \(90\) miles long. Is \(\$6.50\) enough to pay for the gasoline needed? Justify your answer with calculations.

A family fills a small backyard pool with a garden hose. The hose delivers \(0.75\) gallon in \(15\) seconds. Water costs \(\$6.00\) per \(1000\) gallons. a) How many gallons per minute flow from the hose? b) The pool holds \(180\) gallons. How long does it take to fill? c) What does one complete filling cost? d) During a backyard party, the same hose supplies all \(\$2.70\) worth of water used, at its usual flow rate. How many hours did the hose run in total?

For this water-use model, suppose one showerhead uses \(3\) gallons of water per minute and a water-saving showerhead uses \(1.75\) gallons per minute. Water costs \(\$6.00\) per \(1000\) gallons. a) How much water does the water-saving showerhead save during an \(8\)-minute shower? b) Find the cost savings for the \(8\)-minute shower. c) Jan uses the same amount of water with the water-saving showerhead as a \(7\)-minute shower with the other showerhead. How long does Jan shower?

A large water tank is filled at a constant rate. It initially contains \(10\) gallons. After \(10\) minutes, it contains \(35\) gallons. The owner claims, “The \(140\)-gallon tank will be full in another half hour.” Check the claim. Is the stated filling time realistic?

Lucas is charging a tablet. At \(2{:}00\) p.m., the battery level is \(15\%\). At \(2{:}30\) p.m., it is \(75\%\). Assume the tablet charges at a constant rate from \(0\%\) to \(100\%\). a) How many percentage points does the battery level increase per minute? b) How many minutes does a complete charge from \(0\%\) to \(100\%\) take?

Two copy shops charge the following prices: Shop A: \(80\) copies for \(\$6.40\). Shop B: \(150\) copies for \(\$9.00\). a) Find the price per copy at each shop. b) Find the cost of \(400\) copies at each shop. c) How many copies can be purchased for \(\$12.00\) at each shop?

Two cars are tested for gasoline use. Car A uses \(6\) gallons over \(120\) miles. Car B uses \(8\) gallons over \(128\) miles. a) Find each car's gasoline use per \(100\) miles. Which car uses less gasoline? b) How many gallons would each car use on a \(1400\)-mile trip?

Two factory machines produce parts. Machine A makes \(480\) parts in \(4\) hours. Machine B makes \(525\) parts in \(5\) hours. a) Which machine works faster? Justify your answer by finding parts per hour. b) How long does each machine take to complete an order of \(1050\) parts? c) An urgent order must be completed within \(9\) hours. Which machine can complete the order by itself?

A copier in a school library prints \(150\) pages in \(4\) minutes. Assume printing time and page count are proportional. a) How many pages can the copier print in \(10\) minutes? b) How long does it take to print a \(525\)-page document? c) Give one reason why the proportional model might not remain exact for a very large job, such as \(50{,}000\) pages.

During steady rain, a family observes a rain barrel. At \(2{:}00\) p.m., it contains \(12\) gallons. At \(2{:}12\) p.m., it contains \(27\) gallons. Find the average inflow rate during this period in gallons per hour.

A high-capacity pump fills a swimming pool. The pump delivers \(125\,\text{gal}\) every \(30\) seconds. a) Find the pump's rate in gallons per hour. b) The pool holds \(60{,}000\,\text{gal}\). How many hours will it take to fill the pool? c) Filling begins at \(7{:}45\) a.m. At what time will the pool be full?

Three trail signs show the remaining distance to Pine Ridge. <table> <tr><th>Sign</th><th>Distance to Pine Ridge</th></tr> <tr><td>1</td><td>\(21\,\text{mi}\)</td></tr> <tr><td>2</td><td>\(17\,\text{mi}\)</td></tr> <tr><td>3</td><td>\(12\,\text{mi}\)</td></tr> </table> The hiking group takes \(1\) hour to travel from Sign 1 to Sign 2 and \(1.25\) hours to travel from Sign 2 to Sign 3. a) Find the group's average speed on each interval. b) Did the group have the same average speed on both intervals?

A damaged pipe leaks about \(15\,\text{L}\) of water each minute. How many liters leak from the pipe in one full \(24\)-hour day?

A freight elevator can carry up to \(1200\,\text{kg}\) in total and at most \(15\) people. a) If the weight limit is shared equally among \(15\) riders, what is the average share per rider? This is not an individual weight limit. b) A group of \(12\) workers has a combined mass of \(980\,\text{kg}\). May they all ride together? Explain by checking both limits.

A truck uses \(8\) gallons of diesel for every \(100\) miles traveled. Its fuel tank holds \(80\) gallons. How far can the truck travel on a full tank at this rate?

A farmer has \(20\) hazelnut bushes. Each bush produces about \(1500\) nuts. A sample shows that \(100\) nuts have a mass of \(240\,\text{g}\). About how many kilograms of hazelnuts do all the bushes produce?

At a camp, one water container holds \(24\,\text{L}\). Each child drinks about \(3\,\text{L}\) of water per day. a) About how many children can one container supply for one day? b) The camp has \(120\) children. About how many containers are needed each day?

One pear tree produces about \(150\,\text{kg}\) of fruit in a year. The pears are packed into crates that each hold \(15\,\text{kg}\). a) About how many crates can be filled with the pears from one tree? b) An orchard has \(200\) such trees. About how many crates can be filled with the entire harvest?

In a simplified zoo-planning model, use these rounded daily quantities: an adult elephant drinks about \(80\,\text{L}\) of water, one trunkful is modeled as \(16\,\text{L}\), and a newborn elephant drinks about \(10\,\text{L}\) of milk. a) About how many modeled trunkfuls of water does an adult elephant drink each day? b) About how many liters of water do \(5\) adult elephants drink in one day? c) About how many liters of milk does a newborn elephant drink in \(7\) days?

For this walking-rate model, suppose an elephant walks at \(5\) miles per hour and a person walks at \(4\) miles per hour. a) The elephant travels \(20\) miles in one day. How many hours does it walk? b) How far does the person walk in \(4\) hours? c) After \(4\) hours, how much farther has the elephant walked than the person?

In a simplified daily-activity model, suppose an elephant walks \(18\) miles each day at \(6\) miles per hour and spends \(18\) hours per day eating. a) How many hours per day does it spend walking? b) How many hours remain in a \(24\)-hour day for sleeping, bathing, and other activities?

A water-saving showerhead uses \(1\) gallon less water per minute than an older model. A family showers for a total of \(30\) minutes each day. a) How many gallons does the family save each day? b) How many gallons does it save in \(7\) days? c) If \(1000\) gallons cost \(\$4.00\), how much money does the family save in \(10\) weeks?

An older toilet uses \(12\,\text{L}\) of water per flush, while a water-saving toilet uses \(5\,\text{L}\). A person flushes about \(6\) times per day. a) About how many liters does one person save in one day by using the water-saving toilet? b) About how many liters does a four-person family save in \(7\) days? c) About how many liters does the family save in \(365\) days?

A city charges \(\$2.00\) for \(1000\) gallons of water. a) How many cents do \(100\) gallons cost? b) A family uses \(80\) gallons of water per day for washing dishes, laundry, and showers. How many gallons does it use in \(30\) days? c) What does that month's water cost? Give the amount in dollars and cents.

Tim compares two ways to use water when brushing his teeth. <table><tr><th>Method</th><th>Water per brushing</th></tr><tr><td>Leave the tap running</td><td>\(3\) gallons</td></tr><tr><td>Rinse using a cup</td><td>\(0.25\) gallon</td></tr></table> a) Tim brushes twice a day. How many gallons can he save each day by using a cup both times? b) How many gallons can he save in \(100\) days? c) If \(1000\) gallons cost about \(\$3.00\), how much money can he save in \(100\) days?

A family pays \(\$0.20\) for \(40\) gallons of water. A bath uses about \(60\) gallons, while a shower uses \(20\) gallons. a) Find the water cost of one bath. b) How much is saved by showering instead of taking a bath? c) A person usually takes two baths each week. If the person showers instead every time for \(52\) weeks, how much money is saved?

A nursery pays \(\$2.00\) for \(1000\) gallons of water. Flower beds can be watered in two ways: - With watering cans: \(12\) cans holding \(2\) gallons each - With a sprinkler: \(3\) gallons per minute for \(10\) minutes a) How many gallons does each method use? b) What is the water cost of using the sprinkler once? c) The flowers are watered every day for \(30\) days. How much money is saved by always using the watering cans instead of the sprinkler?

A garden owner pays \(\$4.00\) for \(1000\) gallons of tap water. A large watering cart holds \(10\) gallons, and filling a small garden pond requires \(200\) gallons. a) How many cents do \(10\) gallons cost? b) How many cents does the pond filling cost? c) Would using \(25\) full watering carts cost more or less than filling the pond? Explain.

A school pays \(30\) cents for every \(100\) gallons of water. Its restrooms have two types of toilets: - Older toilet: \(3\) gallons per flush - Newer toilet: \(1.5\) gallons per flush a) What does the water for \(100\) flushes of the older toilet cost? b) How much money is saved over \(100\) flushes by using the newer toilet?

A car wash pays \(\$2.00\) for every \(1000\) gallons of water. - A pressure-washer cleaning uses \(60\) gallons. - An automatic wash uses \(150\) gallons. a) How many cents does the water for one pressure-washer cleaning cost? b) How many cents does the water for one automatic wash cost? c) A taxi company has \(10\) cars washed automatically. What is the total water cost?

At a class fitness event, Maya and Noah each run a \(1\)-mile route. Maya takes \(12\) minutes. Noah takes \(10\) minutes. a) How many miles would Maya cover in one hour at the same pace? b) How many miles would Noah cover in one hour at the same pace? c) How many hours would Maya need to cover \(10\) miles at that pace?

A regional train and an express train travel along the same route. - The regional train takes \(2\) minutes to travel \(1\) mile. - The express train takes \(30\) seconds to travel \(1\) mile. a) How many miles does the regional train travel in one hour? b) How many miles does the express train travel in one minute? c) How many miles does the express train travel in one hour?

For a paper-production model, use \(40\) gallons of water per pound for one paper process and \(10\) gallons per pound for a recycled-paper process. A set of \(100\) invitation cards weighs \(4\,\text{lb}\). How much water is saved by making \(25\) of the cards with the recycled-paper process instead of the first process?

An audiobook narrator reads a very long book containing exactly \(1{,}000{,}000\) words. The narrator reads an average of \(125\) words per minute. How many days, hours, and minutes of reading time are needed to finish the book, not including breaks?

A painter paints \(35\,\text{ft}\) of fence in \(5\) hours on Monday. On Tuesday, the painter works for \(3\) hours at the same rate. How many feet of fence does the painter complete during both days altogether?

A gardener uses a hose to fill \(4\) watering cans in \(5\) minutes. Each can holds \(2\) gallons. The same hose fills a large barrel in \(15\) minutes. How many gallons does the barrel hold?

Two families buy a \(14\,\text{lb}\) box of apples for \(\$28\). The Miller family takes \(6\,\text{lb}\), and the Schmidt family takes the rest. If they divide the cost fairly by weight, how much should each family pay?

Leon shops at a farmers market. He pays \(\$6.00\) for \(3\,\text{lb}\) of oranges. He also buys \(2\,\text{lb}\) of bananas, and his total is \(\$11.00\). At the same prices, Sarah buys \(1\,\text{lb}\) of oranges and \(3\,\text{lb}\) of bananas. How much does Sarah pay?

An apple grower harvests \(450\,\text{lb}\) of apples in \(5\) days. He works exactly \(6\) hours each day. On average, how many pounds of apples does he harvest per hour? Show two different ways to calculate the answer.

An older printing machine works \(5\) days for \(8\) hours each day and prints \(4000\) posters. A newer machine prints the same \(4000\) posters in \(4\) days while also running \(8\) hours each day. Find each machine’s average number of posters per hour. Which machine is faster, and by how many posters per hour?

A machine fills \(240\) juice bottles in \(4\) minutes. a) How many bottles does the machine fill in one minute? b) A newer machine fills \(20\) more bottles per minute. How many bottles does the newer machine fill in \(8\) minutes?

Jonas and Sarah run on a track. Jonas runs \(800\,\text{m}\) in \(4\) minutes. Sarah runs \(500\,\text{m}\) in \(2\) minutes. Who runs faster? How far would the faster runner travel in \(10\) minutes at the same rate?

A juice press fills \(12\) bottles in \(20\) minutes. a) How many bottles does it fill in \(60\) minutes? b) How long does it take to fill \(6\) bottles? c) How many bottles does it fill in \(30\) minutes?

A cider mill presses \(3\,\text{qt}\) of cider from \(5\,\text{lb}\) of apples. a) How many quarts of cider can be made from \(20\,\text{lb}\) of apples? b) How many pounds of apples are needed to make \(15\,\text{qt}\) of cider? c) How many pounds of apples are needed to make \(9\,\text{qt}\) of cider?

A printer uses \(120\,\text{mL}\) of ink to print \(40\) posters. a) How many milliliters of ink are needed for \(200\) posters at the same rate? b) How many posters can be printed with \(300\,\text{mL}\) of ink? c) How many posters can be printed with \(30\,\text{mL}\) of ink?

Paul rides his bicycle a total of \(72\,\text{mi}\) in \(6\) hours at a constant speed. He rides \(24\,\text{mi}\) in the morning and the rest in the afternoon. How many hours does he ride in the morning, and how many hours does he ride in the afternoon?

For a school festival, Mr. Weber buys fruit. A \(2\,\text{lb}\) bag of apples costs \(\$4\), and a \(3\,\text{lb}\) bag of pears costs \(\$9\). He wants to buy exactly \(12\,\text{lb}\) of each fruit. How much more will the pears cost than the apples?

At the base of a mountain, the elevation is \(650\,\text{m}\) and the temperature is \(2\,^{\circ}\text{C}\). A station higher up is at \(2250\,\text{m}\). In a simplified model, the temperature drops by \(1\,^{\circ}\text{C}\) for every \(200\,\text{m}\) of elevation gain. What temperature does the model predict at the upper station?

A taxi company charges a base fare of \(\$4.50\) for every ride. It also charges: - daytime rides: \(\$2\) per mile - nighttime rides: \(\$3\) per mile Ms. Maier takes a \(12\,\text{mi}\) daytime ride. Mr. Schmidt takes a \(10\,\text{mi}\) nighttime ride. Who pays more? Calculate both fares.

A hiker walks \(8\) miles in \(2\) hours at a constant rate. The full route is \(20\) miles long. After the first \(2\) hours, how many more hours must the hiker walk?

An excursion boat travels for \(8\) hours each day for \(6\) consecutive days. During that time, it covers \(864\,\text{mi}\). What is the boat’s average distance traveled per hour?

A delivery driver compares two workweeks. During the first week, he drives \(8\) hours per day for \(4\) days and travels \(960\,\text{mi}\). During the second week, he drives \(6\) hours per day for \(5\) days and travels \(990\,\text{mi}\). In which week is his average speed greater?

A grower delivers \(5\) crates of tomatoes with a combined weight of \(60\,\text{lb}\). The grower also delivers \(8\) crates of peppers. The pepper crates weigh \(12\,\text{lb}\) more altogether than the tomato crates. How many pounds heavier is one tomato crate than one pepper crate?

A ferry travels at a constant rate of \(12\) miles per hour. a) How far does the ferry travel in \(4\) hours? b) After \(3\) hours, the ferry has \(24\) miles left to reach its destination. How long is the entire route?

Mia and Jonas take a bicycle trip. Mia rides for \(3\) hours at \(12\,\text{mi/h}\). Jonas rides for \(4\) hours at \(8\,\text{mi/h}\). Who travels farther, and by how many miles?

Mia's step length is \(24\,\text{in}\), and her father's step length is \(36\,\text{in}\). a) How far does each person travel in \(10\) steps? b) Mia's father takes \(2\) steps. How many steps must Mia take to travel the same distance?

Lukas rides his bike at a constant speed of \(14\,\text{mi/h}\). He rides for \(4\) hours on Saturday and \(5\) hours on Sunday. How many miles does he ride altogether?

During an apple harvest, workers pick \(1350\,\text{lb}\) of apples from Field A in \(6\) days. During the same \(6\) days, they pick \(2088\,\text{lb}\) from Field B. What is the average number of pounds picked per day from each field? What is the difference between the two daily averages?

A leaking faucet loses about \(12\) drops of water each minute. a) About how many drops are lost in one hour? b) About how many drops are lost in a full \(24\)-hour day? c) About \(20\) drops equal \(1\,\text{mL}\). About how many milliliters of water are lost in one day?

Lucas reads for \(20\) minutes every evening at a constant rate of \(2\) pages per minute. a) How many pages does he read in one week of \(7\) days? b) Each book in his favorite adventure series has \(160\) pages. At the same rate, how many complete books does he read in \(52\) weeks?

A hiking group covers \(15\,\text{mi}\) per day for \(6\) days. They plan to cover the same total distance on the return trip in only \(5\) days. What average distance must they hike each day on the return trip?

A pump fills a water tank at \(120\,\text{gal}\) per hour and takes exactly \(6\) hours to fill the tank. A stronger pump fills the same tank at \(180\,\text{gal}\) per hour. How long will the stronger pump take, and how many hours shorter is the wait?

A large pump moves \(2240\,\text{gal}\) of water in \(7\) minutes. A small garden pump moves \(48\,\text{gal}\) in \(6\) minutes. How many times as much water per minute does the large pump move as the small pump?

A bakery has two machines for packing dinner rolls. Machine A packs \(960\) rolls in \(4\) hours. Machine B packs the same number of rolls in \(6\) hours. How many more rolls per hour does Machine A pack than Machine B?

Two large haul trucks carry rock at a mine. The blue truck carries \(435\) tons in \(5\) trips. The red truck carries \(656\) tons in \(8\) trips. Which carries more rock per trip, and by how many tons?

Three crates of apples have the same total weight as \(5\) baskets of strawberries. A farmer delivers \(345\) apple crates. How many strawberry baskets would have the same total weight?

At a school field day, the PTA sells pizza. Volunteers prepare \(8\) large pizzas and cut each pizza into \(8\) equal slices. The dough costs \(\$14.50\), the toppings cost \(\$26.80\), and napkins cost \(\$3.50\). The sale must earn a profit of \(\$51.20\) for new sports equipment. What price should be charged for each slice if every slice is sold?

Two printing machines produce \(1560\) flyers altogether. The first machine runs for \(14\) minutes, and the second runs for \(12\) minutes. Both machines print the same number of flyers per minute. How many flyers does each machine print?

At a farmers market, \(12\,\text{lb}\) of apples cost \(\$24\). A note shows these calculations: 1) \(24 \div 12 = 2\) 2) \(2 \times 7 = 14\) a) What quantity is found in the first calculation? b) What does the result \(14\) mean in the second calculation? c) How much would \(10\,\text{lb}\) of the apples cost?

At a print shop, the blue press prints \(120\) pages in \(4\) minutes. The green press prints \(150\) pages in \(6\) minutes. Both work at steady rates. a) Which press prints more pages per minute? b) How many pages would the faster press print in \(15\) minutes? c) How long would the blue press take to print \(300\) pages?

An organic farm grows strawberries. Last year, the field produced an average of \(3\,\text{lb}\) per square yard. This year, the yield increased to \(5\,\text{lb}\) per square yard. Before the farm switched to organic growing methods, the yield was \(1\,\text{lb}\) per square yard. a) How many more pounds does a \(100\,\text{yd}^2\) area produce this year than last year? b) How many more pounds does the same area produce this year than before the switch?

A remote-controlled car and a small robot race for exactly \(1\) minute. The car travels \(25\,\text{m}\) every \(10\) seconds. The robot travels \(2\,\text{m}\) every second. a) How far does the car travel in \(1\) minute? b) How far does the robot travel in \(1\) minute? c) Which one wins, and by how many meters?

A conveyor belt moves packages at \(2\,\text{m}\) per second. A package must travel \(300\,\text{m}\). Is \(2\) minutes enough time for the package to reach the end? Justify your answer with a calculation.

At \(5{:}00\) p.m., a weather station records \(-4\,^{\circ}\text{C}\). Until \(10{:}00\) p.m., the temperature falls by \(3\,^{\circ}\text{C}\) each hour. a) What is the temperature at \(10{:}00\) p.m.? b) At what time is it exactly \(-10\,^{\circ}\text{C}\)?

A laboratory sample is cooled steadily from \(5\,^{\circ}\text{C}\) at \(8{:}00\) a.m. to \(-19\,^{\circ}\text{C}\) at \(2{:}00\) p.m. By how many degrees Celsius does its temperature fall each hour?

A solar water-heating system warms \(12\,\text{gal}\) of water per hour on a cloudy day and \(28\,\text{gal}\) per hour on a sunny day. How much more water does it warm in \(6\) hours on a sunny day? What is the difference after \(9\) hours?

Gardeners planned to plant \(180\) flowers per day and finish a park project in \(12\) days. With help from volunteers, they finished \(4\) days early. On average, how many more flowers per day did they plant than planned?

At a cookout stand, hot dogs cost \(\$6\) for \(8\). They can also be bought individually at the same price per hot dog. a) How much do \(24\) hot dogs cost? b) How much do \(12\) hot dogs cost? c) Explain how you found the price for \(12\) hot dogs without buying only whole packs of eight.

At a game booth, \(20\) marbles cost \(\$4\). a) How many marbles can you buy for \(\$12\)? b) Tim wants \(100\) marbles and has \(\$25\). Does he have enough money? Support your answer with a calculation.

A car uses \(6\,\text{gal}\) of gasoline to travel \(300\,\text{mi}\). a) How much gasoline does it use to travel \(900\,\text{mi}\)? b) How far can it travel with \(30\,\text{gal}\) of gasoline? c) How much gasoline does it use to travel \(150\,\text{mi}\)?

A candle burns at a constant rate. After \(15\) minutes, it is exactly \(12\,\text{mm}\) shorter. The candle was originally \(144\,\text{mm}\) tall. How many hours will the candle burn before it is completely used up?

A copier prints \(250\) flyers in exactly \(6\) minutes \(15\) seconds. At the same rate, how long will it take to print \(1000\) flyers? Give the answer in minutes.

At a farmers market, \(16\,\text{oz}\) of strawberries cost \(\$3.20\). Leo has exactly \(\$1.20\). How many ounces of strawberries can he buy if the price is proportional to the weight?

Liam, Mia, and Tom buy glass craft beads together. All the beads have the same price per ounce. Liam takes \(12\,\text{oz}\), Mia takes \(20\,\text{oz}\), and Tom takes \(18\,\text{oz}\). Liam pays the full bill of \(\$12.50\). How much should Mia and Tom each repay Liam?

Liam wants to buy \(12\) boxes of pasta and \(4\) jars of tomato sauce. He compares prices at three stores: <table> <tr><th>Store</th><th>Pasta quantity</th><th>Pasta price</th><th>Sauce quantity</th><th>Sauce price</th></tr> <tr><td>Fresh Market</td><td>\(3\) boxes</td><td>\(\$2.40\)</td><td>\(2\) jars</td><td>\(\$2.50\)</td></tr> <tr><td>City Shop</td><td>\(4\) boxes</td><td>\(\$3.12\)</td><td>\(4\) jars</td><td>\(\$4.80\)</td></tr> <tr><td>Super Saver</td><td>\(6\) boxes</td><td>\(\$4.68\)</td><td>\(1\) jar</td><td>\(\$1.29\)</td></tr> </table> Find the total cost at each store. Which store is least expensive?

For a class snack, Ms. Wilson needs \(15\) apples and \(5\) bags of oranges. She compares two offers: Offer 1: \(3\) apples cost \(\$1.20\), and one bag of oranges costs \(\$2.45\). Offer 2: \(5\) apples cost \(\$1.90\), and a value pack of \(5\) bags of oranges costs \(\$12.00\). Which offer is less expensive for the full purchase? Find the difference in total price.

Ms. Smith and Mr. Webb clean an office building. Ms. Smith works \(20\) hours per week, and Mr. Webb works \(15\) hours per week. They earn the same hourly wage. Together, they earn \(\$2240\) over \(4\) weeks. a) How much do they earn together in one week? b) What is their hourly wage? c) Mr. Webb claims that he earns more than \(\$1000\) in \(4\) weeks. Is he correct? Show a calculation.

A beekeeper uses \(15\,\text{kg}\) of honey to fill \(30\) jars. a) How many jars can be filled with \(45\,\text{kg}\) of honey at the same rate? b) How many kilograms of honey are needed to fill \(100\) jars?

For trip planning, a ferry company estimates fuel use at \(6\,\text{L}\) per passenger for every \(100\,\text{km}\) traveled. A ferry carries \(850\) passengers on a \(120\,\text{km}\) trip. According to this estimate, how many liters of fuel will the trip use?

Ms. Miller walks \(1.2\,\text{km}\) in \(15\) minutes. Her dog runs \(450\,\text{m}\) across a field in \(5\) minutes. Which one travels more meters per minute? Show the two unit rates.

In a simplified observation, a hummingbird beats its wings \(80\) times per second. A mosquito makes \(15{,}000\) wingbeats in \(30\) seconds. a) Which animal makes more wingbeats per second? b) How many wingbeats would each make during a \(2\)-minute flight at these constant rates?

Two fans are tested. Model A makes \(1200\) revolutions in \(2\) minutes. Model B makes \(15\) revolutions per second. a) Which model rotates faster? Show a calculation using the same time unit. b) How many revolutions does each model make in one-half hour?

The train and road routes from Lakeview to Riverton are both \(120\,\text{km}\) long. The train takes \(1\) hour \(15\) minutes. Ms. Miller drives there in \(1\) hour \(30\) minutes. a) How much time does the train save? b) What is Ms. Miller's average driving speed in kilometers per hour?

A small fountain fills a collection tank. In \(15\) minutes, \(120\,\text{L}\) of water flows into the tank. a) What is the flow rate in liters per minute? b) The empty tank holds \(800\,\text{L}\). How long will it take to fill completely? Give the answer in hours and minutes.

Mr. Webb drives to work and back \(4\) days each week. His one-way commute is \(50\,\text{mi}\). His car averages \(25\,\text{mi}\) per gallon, and gasoline costs \(\$4.10\) per gallon. How much does he spend on gasoline for one week of commuting?

A clock's second hand moves at a constant rate. It takes exactly \(5\,\text{s}\) to move from one number to the next, such as from \(12\) to \(1\). a) How many full revolutions does the second hand make from \(2{:}45\) p.m. to \(3{:}15\) p.m.? b) During that half hour, how much total time does the hand spend moving between \(12\) and \(1\)? Give the result in minutes and seconds.

At a grocery store, \(20\,\text{lb}\) of potatoes cost \(\$30\). Leo writes the following work to find the price of \(8\,\text{lb}\): \(20\,\text{lb}\) costs \(\$30\) \(2\,\text{lb}\) costs \(\$3\) \(8\,\text{lb}\) costs \(\$9\) Check his work. Where is the error, and what is the correct price for \(8\,\text{lb}\)?

A remote-controlled car travels \(12\,\text{m}\) in \(4\) minutes at a constant rate. Priya writes: \(12 \div 4 = 3\,\text{m/min}\) \(30\,\text{s} = 0.5\,\text{min}\) \(3 \div 0.5 = 6\,\text{m}\) Which line is the first incorrect step? Explain the rate error and give the correct distance traveled in \(30\) seconds.

For a class party, \(12\,\text{qt}\) of juice cost \(\$18\). Mateo tries to find the cost of \(5\,\text{qt}\): \(12\,\text{qt}\) cost \(\$18\) \(1\,\text{qt}\) costs \(\$1.80\) \(5\,\text{qt}\) cost \(\$9\) Explain the error in the first calculation and find the correct cost of \(5\,\text{qt}\).

At a farm stand, \(5\) pounds of potatoes cost \(\$10\). A customer wants to buy \(8\) pounds and says, “I will have to pay \(\$18\).” Is the customer correct? Explain with a calculation.

A class takes a three-day hiking trip. Each day, the class hikes for \(4\) hours in the morning and \(2\) hours in the afternoon at an average rate of \(3\,\text{mi/h}\). How many miles does the class hike in all?

Lukas delivers mail by electric bicycle for \(5\) hours per day from Monday through Friday. He rides \(12\,\text{mi}\) each hour. Sarah delivers mail for \(7\) hours per day on \(4\) days and rides \(10\,\text{mi}\) each hour. Who travels farther during the week?

Ms. Miller buys two pieces of fabric from the same bolt at the same price per yard. One piece is \(2\,\text{yd}\) long, and the other is \(6\,\text{yd}\) long. She pays \(\$72\) in all. What is the cost of each piece?

A remote-controlled car moves at a constant rate. Its wheels turn \(10\) times while the car travels \(4\,\text{m}\). A full battery powers \(150\) wheel rotations. How far can the car travel on one full battery?

Lucas and Emilia walk together along a \(120\,\text{m}\) path. Lucas takes \(15\) steps for every \(10\,\text{m}\), while Emilia takes \(18\) steps for every \(10\,\text{m}\). How many more steps does Emilia take over the full path?

A school copier prints \(50\) worksheets in \(3\) minutes at a constant rate. a) How many worksheets does it print in \(15\) minutes? b) How many minutes does it take to print \(300\) worksheets?

A class plans a bicycle trip to a lake \(60\,\text{mi}\) away. The group rides \(12\,\text{mi}\) each hour. a) How far has the group traveled after \(2\) hours? b) The group takes a long break after \(3\) hours. How far is it from the lake then? c) How many hours of riding time are needed for the entire trip?

A truck is delivering a load to a city \(260\,\text{mi}\) away. It travels at \(65\,\text{mi/h}\). a) How far has the truck traveled after \(3\) hours? b) After how many hours has the truck traveled exactly half the total distance? c) A faster delivery van travels the same route at \(80\,\text{mi/h}\). How far is the van from the city after \(3\) hours?

Two farms compare strawberry yields. Sunny Acres harvests \(480\,\text{lb}\) from \(12{,}000\,\text{ft}^2\). Fresh Fields harvests \(900\,\text{lb}\) from \(20{,}000\,\text{ft}^2\). Which farm has the greater yield per \(1000\,\text{ft}^2\)? Show both rates.

A seller offers three rectangular garden plots: 1) \(40\,\text{ft} \times 50\,\text{ft}\) for \(\$12{,}000\) 2) \(60\,\text{ft} \times 30\,\text{ft}\) for \(\$9000\) 3) \(25\,\text{ft} \times 80\,\text{ft}\) for \(\$11{,}000\) Find the price per square foot for each plot. Order the plots from least expensive to most expensive by unit price.

A print shop's copier prints \(p\) pages in \(t\) minutes at a steady rate. Both numbers are positive. a) Write its printing rate in pages per minute. b) Write an expression for the number of minutes it takes to print \(x\) pages at the same rate. c) The copier prints \(180\) pages in \(4.5\) minutes. Find its printing rate. d) At that rate, how long will it take to print \(540\) pages?

The number line begins at \(0\) and is divided into \(20\) equal intervals. The endpoint is labeled “?”. Point \(A\) is marked on the number line. Find the value at “?” in each case. a) Point \(A\) represents \(0.8\). b) Point \(A\) represents \(0.08\). c) Point \(A\) represents \(\frac{2}{5}\).

The diagram shows the dimensions of a wall that needs wallpaper. You can choose between two types of rolls: <table><tr><th>Wallpaper</th><th>Coverage per roll</th><th>Price per roll</th></tr><tr><td>Type A</td><td>\(50\,\text{ft}^2\)</td><td>\(\$12.50\)</td></tr><tr><td>Type B</td><td>\(75\,\text{ft}^2\)</td><td>\(\$18.00\)</td></tr></table> Find the total cost for each wallpaper type. Which type costs less? Assume each roll must be purchased whole.

The graph shows the number of pages a printer produces at a constant rate. a) What is the unit rate in pages per minute? b) At the same rate, how many pages will the printer produce in \(6\) minutes? c) How many minutes will it take to produce \(150\) pages?

Lines a and b show the distances traveled by two hikers moving at constant speeds. Time is measured in hours and distance in miles. a) Find each hiker’s unit rate. b) Which hiker is faster, and by how many miles per hour?

A pump is described by the table. A second pump is described by the graph. <table> <tr><th>Time (minutes)</th><th>Water added (gallons)</th></tr> <tr><td>\(2\)</td><td>\(50\)</td></tr> <tr><td>\(5\)</td><td>\(125\)</td></tr> </table> a) Find the unit rate represented by the table. b) The graph has a marked point P. Read the coordinates of P and use them to find the graph's unit rate. c) Do the table and graph represent the same constant rate? Explain.

A machine fills bottles at a constant rate. <table> <tr><th>Time (minutes)</th><th>Bottles filled</th></tr> <tr><td>0</td><td>0</td></tr> <tr><td>2</td><td>10</td></tr> <tr><td>4</td><td>20</td></tr> <tr><td>6</td><td>30</td></tr> </table> Talia predicts that the machine will fill \(32\) bottles in \(8\) minutes because both the time and bottle count should go up by \(2\). Explain why this reasoning is incorrect and find the correct number of bottles.

A team needs at least \(10\) water bottles. A store sells only \(4\)-packs for \(\$6\) and \(7\)-packs for \(\$11\). Which whole packs should the team buy to pay the least? How much will they cost?

On a number line, point \(A=\frac{5}{6}\) and point \(B=1\frac{1}{4}\) are exactly \(5\,\text{cm}\) apart. a) How long is the interval from \(0\) to \(1\) on this number line? b) What number is located exactly \(2\,\text{cm}\) to the right of point \(B\)? Give the result as a simplified fraction or mixed number.

A cyclist rides at a constant speed of \(23.4\,\text{km/h}\). A runner covers \(400\,\text{m}\) in \(1\) minute \(15\) seconds. Use \(1\,\text{m/s}=3.6\,\text{km/h}\). a) How many meters does the cyclist travel per second? b) Who travels farther in \(10\) minutes? Find each distance in meters.

A school break begins at \(9{:}35\) a.m. and ends at \(9{:}55\) a.m. a) Through what angle does the minute hand move during the break? b) Through what angle does the hour hand move during the same time? c) Find the smaller angle between the two hands at exactly \(9{:}55\) a.m.

A faulty toilet leaks about \(0.5\) gallon of water per minute. Water costs \(\$6.00\) per \(1000\) gallons. a) How many gallons are wasted in one full day? b) What does the leak cost per day? c) After how many complete days will the accumulated cost first exceed the \(\$18.50\) price of a replacement part?

A passenger train travels at a constant speed of \(60\,\text{mi/h}\). Use \(1\,\text{mi}=5280\,\text{ft}\) and \(1\,\text{h}=3600\,\text{s}\). a) Find the train's speed in feet per second. b) The train is \(440\,\text{ft}\) long. How many seconds does it take to completely cross a bridge that is \(1320\,\text{ft}\) long? The crossing is complete when the back of the train leaves the bridge. c) How many miles does a passenger travel in \(12\) minutes?

A pipe leaks about \(0.2\,\text{gal}\) of water every \(5\) minutes. a) How many gallons of water leak out in one week? b) An empty \(3\)-gallon bucket is placed under the leak at the beginning of a day. The bucket must be empty again at the end of the day. How many times must the bucket be emptied during that day so that it never overflows? Justify your answer.

Harvesting a strawberry field by hand used to take \(165\) minutes, and sorting the berries took another \(75\) minutes. A new machine completes both jobs in \(40\) minutes. a) How long did both jobs take before the machine was used? b) How many minutes does the machine save? c) How many times as great as the manual work rate is the machine’s work rate?

A climber is at a summit \(4100\,\text{m}\) above sea level, where the temperature is \(-14\,^{\circ}\text{C}\). The climber descends to a shelter where it is \(-6\,^{\circ}\text{C}\). In a simplified model, the temperature rises by \(1\,^{\circ}\text{C}\) for every \(250\,\text{m}\) of descent. What is the shelter's elevation?

A school trip includes \(88\) students and \(4\) teachers. Two bus sizes are available: - Bus A: \(20\) seats for \(\$130\) - Bus B: \(30\) seats for \(\$180\) a) Sari claims, “The larger bus costs less per seat.” Check the claim. b) Find the least expensive combination of buses that can carry all \(92\) people. Give the total cost.

A school festival needs at least \(115\) apples. A store offers two packages: - Bag A: \(15\) apples for \(\$3.00\) - Bag B: \(25\) apples for \(\$4.00\) a) Which bag has the lower cost per apple? Explain. b) What combination of bags gives at least \(115\) apples for the least total cost? Find the cost.

A scout group of \(54\) people is planning an overnight trip. Two types of tents are available: - Small tent: sleeps \(4\) people and costs \(\$15\) per night. - Large tent: sleeps \(6\) people and costs \(\$20\) per night. a) Show which tent type has the lower cost per sleeping space. b) Find the least expensive combination of tents that provides space for all \(54\) people. What is the total cost?

A gardener buys two bags of the same potting soil at the same price per pound. The first bag costs \(\$10.50\), and the second bag costs \(\$12.00\). Together, the bags weigh \(75\,\text{lb}\). a) How many pounds does each bag weigh? b) A third bag of the same soil weighs \(50\,\text{lb}\). How much does it cost?

An organic farm sells \(10\,\text{lb}\) bags of potatoes at the same price per bag. The farm earns \(\$180\) from morning sales and \(\$264\) from afternoon sales. It sells exactly \(7\) more bags in the afternoon than in the morning. How many pounds of potatoes are sold that day?

Two hiking groups walk a combined distance of \(46\,\text{mi}\). Group B walks \(4\,\text{mi}\) farther than Group A. Group A walks at \(3\,\text{mi/h}\), and Group B walks at \(5\,\text{mi/h}\). How many hours does each group walk?

Two trucks carry a combined total of \(1260\) tons of sand. Yellow carries \(60\) tons more than Blue. Blue carries \(15\) tons per trip, and Yellow carries \(22\) tons per trip. How many trips does each truck make?

A hardware store sells a full roll of underground cable for \(\$630\). The price per foot is constant throughout the roll. A gardener buys \(12\,\text{ft}\) of cable, leaving cable worth \(\$450\) on the roll. How many feet of cable were on the roll at first?

A runner covers \(200\,\text{m}\) in \(25\) seconds. a) What is the average speed in meters per second? b) A student says, “If the runner could hold that speed for \(10\,\text{km}\), the run would take less than \(25\) minutes.” Check this calculation. Use \(1\,\text{km}=1000\,\text{m}\) and \(1\) minute \(=60\) seconds. c) Why might the predicted time not be realistic?

Ms. Miller is seeding a \(15{,}000\,\text{ft}^2\) lawn. The seed label recommends \(2\) to \(3\,\text{lb}\) of seed per \(1000\,\text{ft}^2\). Seed is sold in \(2\)-pound bags, and she will spread the entire contents of every bag she buys. What is the minimum number and maximum number of bags she can buy while staying within the recommended rate?

A rectangular sports field is \(315\,\text{ft}\) long and \(200\,\text{ft}\) wide. Fertilizer is applied at a rate of \(4\,\text{lb}\) for every \(1000\,\text{ft}^2\). Each bag contains \(25\,\text{lb}\) and costs \(\$32\). What is the total cost of buying enough whole bags for the field?

A park rents lawn space for a festival at \(\$4356\) per acre. Smaller spaces cost the same amount per square foot. A rectangular space \(20\,\text{ft}\) wide costs \(\$140\) to rent. How long is it? Use \(1\) acre \(=43{,}560\,\text{ft}^2\).