Exploring Real-Life Rates of Change: Graph & Analyze

A car travels 60 miles in 1 hour and 90 miles in 1.5 hours. What is the rate of change in miles per hour for each segment of the trip? Which segment has a higher rate of change?

• Both segments have a rate of change of 60 miles/hour.

• The first segment has a rate of change of 50 miles/hour and the second 60 miles/hour.

• The first segment has a rate of change of 70 miles/hour and the second 80 miles/hour.

• The first segment has a rate of change of 60 miles/hour and the second 70 miles/hour.

A plant grows 3 inches in the first week and 5 inches in the second week. What is the rate of growth for each week? How do these rates compare?

• First week: 3 inches/week, Second week: 6 inches/week. First week is faster.

• First week: 2 inches/week, Second week: 4 inches/week. Both weeks are equal.

• First week: 3 inches/week, Second week: 5 inches/week. Second week is faster.

• First week: 5 inches/week, Second week: 3 inches/week. Second week is faster.

Two friends are saving money. Friend A saves $20 per week, while Friend B saves $15 per week. After how many weeks will Friend A have saved more than Friend B?

• 1 week

• 3 weeks

• 2 weeks

• 4 weeks

A cyclist rides 12 miles in 30 minutes and then 18 miles in 45 minutes. Calculate the rate of change in miles per hour for both segments. Which segment has a greater rate of change?

• The second segment has a rate of change of 22 miles per hour.

• The first segment has a greater rate of change at 30 miles per hour.

• Both segments have a rate of change of 24 miles per hour.

• Both segments have a rate of change of 20 miles per hour.

A factory produces 200 toys in 4 hours and 300 toys in 6 hours. What is the rate of production for each time period? Which time period has a higher production rate?

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

• The production rate is 40 toys per hour for both periods.

• The second period has a production rate of 70 toys per hour.

• The first period has a higher production rate of 60 toys per hour.

A runner completes a 5K race in 25 minutes and a 10K race in 55 minutes. What is the average speed in miles per hour for each race? How do the speeds compare?

• 5K average speed: 6.00 mph, 10K average speed: 5.50 mph. 10K is faster than 5K.

• 5K average speed: 7.44 mph, 10K average speed: 6.78 mph. 5K is faster than 10K.

• 5K average speed: 8.00 mph, 10K average speed: 7.00 mph. Both speeds are equal.

• 5K average speed: 7.00 mph, 10K average speed: 7.44 mph. 10K is faster than 5K.

A student reads 30 pages in 1 hour and 50 pages in 2 hours. What is the reading rate for each hour? Which reading rate is faster?

• 25 pages/hour is faster than 30 pages/hour.

• 30 pages/hour is faster than 25 pages/hour.

• 30 pages/hour is the same as 30 pages/2 hours.

• 50 pages/hour is faster than 30 pages/hour.

A water tank fills at a rate of 10 gallons per hour for the first 3 hours and 15 gallons per hour for the next 2 hours. What is the rate of change in gallons per hour for each period? Which period has a higher rate?

• The first period has a rate of 10 gallons per hour, and the second period has a rate of 10 gallons per hour. Both periods have the same rate.

• The first period has a rate of 15 gallons per hour, and the second period has a rate of 20 gallons per hour. The second period has a higher rate.

• The first period has a rate of 5 gallons per hour, and the second period has a rate of 10 gallons per hour. The first period has a higher rate.

• The first period has a rate of 10 gallons per hour, and the second period has a rate of 15 gallons per hour. The second period has a higher rate.

A chef prepares 5 dishes in 2 hours and 8 dishes in 3 hours. What is the rate of dish preparation for each time frame? How do these rates compare?

• Rate for 2 hours: 2.2 dishes/hour; Rate for 3 hours: 2.5 dishes/hour; 2.5 < 2.2

• Rate for 2 hours: 2 dishes/hour; Rate for 3 hours: 2.5 dishes/hour; 2.5 > 2

• Rate for 2 hours: 3 dishes/hour; Rate for 3 hours: 2 dishes/hour; 3 > 2

• Rate for 2 hours: 2.5 dishes/hour; Rate for 3 hours: 2.67 dishes/hour; 2.67 > 2.5

A smartphone battery drains from 100% to 40% in 2 hours and then from 40% to 10% in 1 hour. What is the rate of battery drain for each time period? Which period has a higher rate of drain?

• The second period drains at 20% per hour.

• The first period drains at 25% per hour.

• The first period drains at 40% per hour.

• Both periods have the same rate of drain at 30% per hour.