1960 AMC 12 Problem 34
Attempt Problem 34 of the 1960 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 1960 AMC 12 solutions, or check the answer key.
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34.
Two swimmers, at opposite ends of a -foot pool, start to swim the length of the pool, one at the rate of feet per second, the other at feet per second. They swim back and forth for minutes. Allowing no loss of time at the turns, find the number of times they pass each other.
Answer: C
Small hint:
Reflect the pool each time a swimmer turns so both paths become straight
Big hint:
The joint position pattern repeats every seconds; inspect one full cycle, including endpoint coincidences
Solution:
The faster swimmer’s position repeats every seconds, and the slower swimmer’s position repeats every seconds. Thus their joint position pattern repeats every seconds. During one such cycle, their positions coincide at seconds. The keyed interpretation counts the simultaneous turn at the endpoint when as one of these encounters. Thus there are counted encounters per cycle and cycles in minutes, giving
Therefore, the correct answer is C.