Problem 80.

You travel on the highway at a rate of 60 mph for 1 hour and at 50 mph for 2 hours and 40 mph for 3 hours. What is the total distance you have traveled? What is your average speed during the trip?

Solution:

We divide the whole trip into three intervals:

(1) travel at a speed of 60 mph for 1 hour.

(2) travel at a speed of 50 mph for 2 hours,

(3) travel at a speed of 40 mph for 3 hours.

For each interval we know speed and time, then we can easily find the traveled distance (for each interval). The distance is equal to the product of time and speed (motion with constant velocity):

Then

(1) speed is 60 mph, time is 1 hour. Then

(2) speed is 50 mph, time is 2 hour. Then

(3) speed is 40 mph, time is 3 hour. Then

Then the total traveled distance is

The average speed is defined as the ratio of total traveled distance and the total traveled time. The total traveled time is

Now we can find the average speed: