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1966 AMC 12 Question 37

AMC12 · 1966 AMC 12

Question 37

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 $h$ be the number of hours needed by Alpha and Beta, working together, to do the job. Then $h$ equals:
  1. $\dfrac52$
  2. $\dfrac32$
  3. $\dfrac43$
  4. $\dfrac54$
  5. $\dfrac34$