1966 AHSME Problems/Problem 37
Contents
Problem
Three men, Alpha, Beta, and Gamma, working together, do a job in 6 hours less time than Alpha alone, in 1 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:
Solution
Solution 2
Let ,, denote the number of hours needed by Alpha, Beta, Gamma, respectively. We also have their respective efficiency , , and . Thus we get the equations Equating the first equations gets Substituting the new relation along with the third equation into the first equation gets Solving the quadratic gets or . Since , is the only legit solution.
Thus and , .
~ Nafer
See also
1966 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 36 |
Followed by Problem 38 | |
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