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Math Help - work problem

  1. #1
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    work problem

    Hello,
    Can someone help explain the method to solve the following problem?

    If Sam can do a job in 4 days that Bob can do in 6 days, and Tom can do it in 2 days, then how long would the job take if they all worked together?

    I can get get close by using pictures and working through it that way, but I'm looking for the way to set it up in a formula.

    Thanks for your help.
    BryanC
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  2. #2
    Super Member wingless's Avatar
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    If Sam can do a job in 4 days, he can do 1/4 of the job in a day.
    If Bob can do it in 6 days, he can do 1/6 of the job in a day.
    If Tom can do it in 2 days, he can do 1/2 of the job in a day.

    Together, they can do \frac{1}{2} + \frac{1}{6} + \frac{1}{4} = \frac{11}{12} of the job in a day. If they can do \frac{11}{12} of the job in a day, they can do the job in \frac{12}{11} days.
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  3. #3
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    Thanks Wingless... One followup question.

    I understand the method to achieve 11/12 of the job in a day. Can you explain how you arrived at 12/11 as the final solution? Thanks Again. I'm sorry for the stupid question.
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  4. #4
    Super Member wingless's Avatar
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    You can achieve it using a simple proportion.

    <br />
          \begin{array}{cc}<br />
Day ~~&~~ Job \\ \hline 1 ~~&~~ \frac{11}{12} \\ x ~~&~~ 1<br />
          \end{array}<br />

    In words: If they can do \frac{11}{12} of the job in 1 day, how many days will it take to do the job completely?

    1\cdot1 = \frac{11}{12}\cdot x

    x = \frac{12}{11}
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