Real-World Rates: Comparing Change & Linear Relationships

A car travels 60 miles in 1 hour, while a bike travels 15 miles in 1 hour. What is the rate of change in miles per hour for both vehicles? How do their rates compare?

• Car: 50 mph, Bike: 20 mph. Car is slower.

• Car: 70 mph, Bike: 10 mph. Bike is faster.

• Car: 60 mph, Bike: 15 mph. Car is faster.

• Car: 60 mph, Bike: 15 mph. Both are equal.

A factory produces 200 toys in 4 hours, while another factory produces 150 toys in 3 hours. What is the rate of change for each factory in toys per hour? Which factory has a higher production rate?

• Both factories have the same production rate of 50 toys per hour.

• Factory A produces 50 toys per hour, while Factory B produces 40 toys per hour.

• Factory B produces 45 toys per hour.

• Factory A produces 60 toys per hour.

A runner completes a 5K race in 25 minutes, while another runner completes it in 30 minutes. What is the rate of change in minutes per kilometer for each runner? Who runs faster?

• First runner: 4 minutes/km, Second runner: 5 minutes/km. First runner runs slower.

• First runner: 6 minutes/km, Second runner: 7 minutes/km. Second runner runs faster.

• First runner: 5 minutes/km, Second runner: 6 minutes/km. First runner runs faster.

• First runner: 5 minutes/km, Second runner: 5 minutes/km. Both runners are equally fast.

A water tank fills at a rate of 10 gallons per minute, while another tank fills at a rate of 15 gallons per minute. How much water is in each tank after 10 minutes? Which tank fills faster?

• Tank 1: 90 gallons, Tank 2: 140 gallons; Both tanks fill at the same rate.

• Tank 1: 110 gallons, Tank 2: 160 gallons; Tank 1 fills faster.

• Tank 1: 100 gallons, Tank 2: 150 gallons; Tank 2 fills faster.

• Tank 1: 80 gallons, Tank 2: 120 gallons; Tank 1 fills faster.

A student reads 30 pages in 1 hour, while another student reads 45 pages in 1.5 hours. What is the rate of change in pages per hour for each student? Who reads more pages per hour?

• The first student reads 60 pages per hour, while the second reads 45 pages per hour.

• The first student reads 30 pages per hour, while the second reads 30 pages per hour.

• Both students read the same number of pages per hour.

• The first student reads 45 pages per hour, while the second reads 30 pages per hour.

A train travels 120 miles in 2 hours, while a bus travels 90 miles in 1.5 hours. What is the rate of change in miles per hour for each vehicle? Which one is faster?

• The train travels at 70 mph and the bus at 60 mph; the train is faster.

• The train travels at 60 mph and the bus at 50 mph; the bus is faster.

• The train travels at 80 mph and the bus at 40 mph; the train is faster.

• Both the train and the bus travel at 60 miles per hour; neither is faster.

A gardener plants 50 flowers in 2 hours, while another gardener plants 75 flowers in 3 hours. What is the rate of change in flowers per hour for each gardener? Who plants more flowers per hour?

• Both gardeners plant the same number of flowers per hour.

• The first gardener plants more flowers than the second.

• The first gardener plants 25 flowers per hour.

• The second gardener plants 30 flowers per hour.

A chef prepares 40 meals in 2 hours, while another chef prepares 60 meals in 3 hours. What is the rate of change in meals per hour for each chef? Which chef is more efficient?

• Chef A is more efficient.

• Chef B is more efficient.

• Both chefs are equally efficient.

• Chef A prepares more meals overall.

A cyclist rides 24 miles in 1.5 hours, while a jogger runs 10 miles in 1 hour. What is the rate of change in miles per hour for each? Who is moving faster?

• The cyclist is moving faster at 20 miles per hour.

• Both are moving at the same speed of 12 miles per hour.

• The cyclist is moving faster at 16 miles per hour.

• The jogger is moving faster at 10 miles per hour.

A bookstore sells 120 books in 4 days, while an online store sells 200 books in 5 days. What is the rate of change in books sold per day for each store? Which store sells more books per day?

• The bookstore sells 25 books per day; the online store sells 35 books per day.

• The bookstore sells 40 books per day; the online store sells 50 books per day.

• The bookstore sells 20 books per day; the online store sells 30 books per day.

• The bookstore sells 30 books per day; the online store sells 40 books per day. The online store sells more books per day.