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1965 AMC 12 Question 38

AMC12 · 1965 AMC 12

Question 38

$A$ takes $m$ times as long to do a piece of work as $B$ and $C$ together; $B$ takes $n$ times as long as $C$ and $A$ together; and $C$ takes $x$ times as long as $A$ and $B$ together. Then $x,$ in terms of $m$ and $n,$ is:
  1. $\dfrac{2mn}{m+n}$
  2. $\dfrac1{2(m+n)}$
  3. $\dfrac1{m+n-mn}$
  4. $\dfrac{1-mn}{m+n+2mn}$
  5. $\dfrac{m+n+2}{mn-1}$