1957 AHSME Problems/Problem 20

Problem

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:

$\textbf{(A)}\ 47\frac{7}{19}\qquad \textbf{(B)}\ 47\frac{1}{4}\qquad \textbf{(C)}\ 47\frac{1}{2}\qquad \textbf{(D)}\ 47\frac{11}{19}\qquad \textbf{(E)}\ \text{none of these}$

Solution

Suppose the first half of the trip's distance is called $x$ . Then the time for the first half is $\dfrac{x}{50},$ and the second half's time is $\dfrac{x}{45}$ , so the total time is $\dfrac{x}{50}+\dfrac{x}{45}$ , so the speed is $\dfrac{2x}{\frac{x}{50}+\frac{x}{45}}=\dfrac{2x}{\frac{19x}{450}}=2x \cdot \dfrac{450}{19x}=\dfrac{900}{19}=47\dfrac{7}{19}$ , so the answer is $\boxed{\textbf{(A)}}$ .

1957 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 19	Followed by Problem 21
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1957 AHSME Problems/Problem 20

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