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# Averages part I

## Question

Examine the following two problems:

A fellow travels from city A to city B. For the first hour, he drove at the constant speed of 20 miles per hour. Then he (instantaneously) increased his speed and, for the next hour, kept it at 30 miles per hour. Find the average speed of the motion.

A fellow travels from city A to city B. The first half of the way, he drove at the constant speed of 20 miles per hour. Then he (instantaneously) increased his speed and traveled the remaining distance at 30 miles per hour. Find the average speed of the motion.

These two problems are often confused. Calculate the solutions of the two problems. What is the difference in value between the two questions?

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In the first problem, the fellow travels 50 miles in two hours, so the average speed is 25 mph.

In the second problem, he travels a certain distance, but the first half takes 50% longer than the second half. So say he travelled for five hours. Then he spent three hours driving 20 mph and two hours driving 30 mph. So he would have driven a total of 120 miles in five hours, and the average speed is 24 mph.

Edited by gavinksong

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