1955 AMC 12 Problem 10

Attempt Problem 10 of the 1955 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 1955 AMC 12 solutions, or check the answer key.

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

10.

How many hours does it take a train traveling at an average rate of 4040 mph between stops to travel aa miles if it makes nn stops of mm minutes each?
3a+2mn120\dfrac{3a+2mn}{120}
3a+2mn3a+2mn
3a+2mn12\dfrac{3a+2mn}{12}
a+mn40\dfrac{a+mn}{40}
a+40mn40\dfrac{a+40mn}{40}
Answer: A
Concepts:rate-time-distanceunit conversionalgebraic expression
Small hint:
The moving time is a40\frac{a}{40} hours
Big hint:
Convert the total stopping time mnmn from minutes to hours before adding
Solution:
The train moves for a40\frac{a}{40} hours and is stopped for mn60\frac{mn}{60} hours. Hence the total time is a40+mn60=3a+2mn120. \frac a{40}+\frac{mn}{60} =\frac{3a+2mn}{120}.
Thus, the correct answer is A.
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