Modeling Rates of Change: Quiz

Problem 1

A testing organization runs cars through varied terrain of trail, road, and pavement. Over one section of trail, the car travels for 5 minutes at 15 miles per hour. Over a dirt road, the car travels at 35 miles per hour for 10 minutes. On paved road, the car travels 65 miles per hour for 15 minutes.

  1. What is the total time spent on the course?
  2. What is the total distance traveled?
  3. What is the average speed of the car?

Answers, problem 1

  1. Add up all the times: 5 minutes + 10 minutes + 15 minutes = 30 minutes
  2. Distance travelled at 15 miles per hour = 15 miles/1hr * 1hr/60 minutes * 5 minutes = 1.25 miles
    Distance travelled at 35 miles per hour = 35 miles/1hr * 1hr/60 minutes * 10 minutes = 5.833 miles
    Distance travelled at 65 miles per hour = 65 miles/1hr * 1hr/60 minutes * 15 minutes = 16.25 miles
    Therefore total distance travelled is 1.25 + 8.833 + 16.25 = 23.33333333 miles
  3. Average speed of the car is (total distance)/(total time) = 23.333 miles * 30 minutes * 60 minutes/1hr = 46.66666666 miles per hour

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