$A$ can do a piece of work in $12$ days and $B$ can do it in $18$ days. Working together, they will finish…

$A$ can do a piece of work in $12$ days and $B$ can do it in $18$ days. Working together, they will finish it in:
  1. $6$ days
  2. $\dfrac{36}{5}$ days
  3. $8$ days
  4. $15$ days

Solution

Combined rate $= \dfrac{1}{12} + \dfrac{1}{18} = \dfrac{3 + 2}{36} = \dfrac{5}{36}$/day. Time $= \dfrac{36}{5}$ days $= 7.2$ days.

Asked in: IMO

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