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
\[\frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{2}{C}\Longarrowright \frac{1}{A}+\frac{1}{B}=\frac{1}{C}\] (Error compiling LaTeX. Unknown error_msg)
Substituting the third equation into the first equation yields
See also
1966 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 36 |
Followed by Problem 38 | |
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