1966 AMC 12 Problem 37
Attempt Problem 37 of the 1966 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 1966 AMC 12 solutions, or check the answer key.
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37.
Three men, Alpha, Beta, and Gamma, working together, do a job in hours less time than Alpha alone, in hour less time than Beta alone, and in one-half the time needed by Gamma when working alone. Let be the number of hours needed by Alpha and Beta, working together, to do the job. Then equals:
Answer: C
Small hint:
Let be the time all three take together
Big hint:
Their individual times are and ; add reciprocal rates
Solution:
If all three together take hours, then This simplifies to so Alpha and Beta alone take and hours, so their combined rate is Hence
Therefore, the correct answer is C.