1957 AMC 12 Problem 20

Question

A man makes a trip by automobile at an average speed of

50

mph. He returns over the same route at an average speed of

45

mph. His average speed for the entire trip is:

47\frac7{19}

mph

47\frac14

mph

47\frac12

mph

47\frac{11}{19}

mph

none of these

Use a convenient one-way distance and divide total distance by total time

For equal distances the arithmetic mean of the two speeds is not the average speed

Let each leg have distance

d.

The average speed, in miles per hour, is

\begin{aligned} \frac{2d}{\frac{d}{50}+\frac{d}{45}} &=\frac{2}{\frac{1}{50}+\frac{1}{45}}\\ &=\frac{900}{19}\\ &=47\frac7{19}. \end{aligned}

Thus, the correct answer is A.

Problem 20 in other years