1965 AMC 12 Problem 28
Attempt Problem 28 of the 1965 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 1965 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
An escalator (moving staircase) of uniform steps visible at all times descends at constant speed. Two boys, and walk down the escalator steadily as it moves, negotiating twice as many escalator steps per minute as reaches the bottom after taking steps while reaches the bottom after taking steps. Then is:
Answer: B
Small Hint:
Let ’s stepping rate be and the escalator rate be
Big Hint:
Equate and
Solution:
Let take steps per minute, so takes and let the escalator contribute steps per minute. Their travel times are and Thus This gives and then
Therefore, the correct answer is B.
Problem 28 in Other Years
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