1962 AMC 12 Problem 10

Attempt Problem 10 of the 1962 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 1962 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

10.

A man drives

150

miles to the seashore in

3

hours and

20

minutes. He returns from the shore to the starting point in

4

hours and

10

minutes. Let

r

be the average rate for the entire trip. Then the average rate for the trip going exceeds

r,

in miles per hour, by:

5

4\dfrac12

4

2

1

Use total distance divided by total time for

r

The outbound time is

\frac{10}{3}

hours and the round-trip time is

\frac{15}{2}

hours

The outbound rate is

\frac{150}{\frac{10}{3}}=45

miles per hour. The entire trip covers

300

miles in

3\frac13+4\frac16=7\frac12

hours, so

r=\frac{300}{\frac{15}{2}}=40.

The difference is

45-40=5.

Thus, the correct answer is A.

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