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Math Help - 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 \frac{1}{21} of the job, man 2 does \frac{1}{28} of the job, and the boy does \frac{1}{48} of it.

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

     = \frac{5}{48}.


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

    \frac{5}{48} : 1

    5 : 48

    1 : \frac{48}{5}

    1 : 9.6.


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