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Thread: Word Problem

  1. #1
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    Word Problem

    A man can do a certain task in 21 hours, another can do the task in 28 hours, and a boy can do the task in 48 hours. How long will it take to do the task if all work together?
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  2. #2
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    Every hour man 1 does $\displaystyle \frac{1}{21}$ of the job, man 2 does $\displaystyle \frac{1}{28}$ of the job, and the boy does $\displaystyle \frac{1}{48}$ of it.

    So that means, every hour $\displaystyle \frac{1}{21} + \frac{1}{28} + \frac{1}{48}$ of the job gets done

    $\displaystyle = \frac{5}{48}$.


    So if we set up a ratio (amount of job : hours)...

    $\displaystyle \frac{5}{48} : 1$

    $\displaystyle 5 : 48$

    $\displaystyle 1 : \frac{48}{5}$

    $\displaystyle 1 : 9.6$.


    So they will finish the job in $\displaystyle 9.6$ hours, or 9 hours 36 mins.
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