1952 AMC 12 Problem 10

Attempt Problem 10 of the 1952 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1952 AMC 12 solutions, or check the answer key.

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10.

An automobile went up a hill at a speed of

10

miles an hour and down the same distance at a speed of

20

miles an hour. The average speed for the round trip was:

12\dfrac12

mph

13\dfrac13

mph

14\dfrac12

mph

15

mph

None of these

Use equal distances rather than averaging the two speeds directly

For a one-mile trip each way, divide the total distance

2

by the total time

\frac{1}{10}+\frac{1}{20}

For one mile in each direction, the total time is

\frac1{10}+\frac1{20}=\frac3{20}

hour. Thus the average speed is

\frac{2}{\frac{3}{20}}=\frac{40}{3} =13\frac13\text{ mph}.

Thus, the correct answer is B.

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