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Math Help - Calculating Work Done.

  1. #1
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    Question Calculating Work Done.

    I am having difficulty with the following problem:
    Mr.Boone can do a job in 10 days . A helper joins him after 3 days and together they work for 4 days to complete the task.How many days would it take the helper to do the task alone ?
    Note : the ans is 13.33

    I know the formula for time taken for two people when working together is
    T = 1/ ( (1/x) + (1/y))
    But i cant manage to compensate mr boon for the 3 days he worked on his own. How would i do that ??
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  2. #2
    MHF Contributor Reckoner's Avatar
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    Re: Calculating Work Done.

    Quote Originally Posted by MikeNoob View Post
    Mr.Boone can do a job in 10 days . A helper joins him after 3 days and together they work for 4 days to complete the task.How many days would it take the helper to do the task alone ?
    Mr. Boone can do one job in ten days. So after 3 days, he has already done 3/10ths of the job. Working together, it takes 4 days to finish the remaining 7/10ths. So we subtract the two rates to find the helper's work rate:

    \frac{7/10\ \mathrm{jobs}}{4\ \mathrm{days}}-\frac{1\ \mathrm{job}}{10\ \mathrm{days}} = \frac7{40}-\frac4{40}=\frac{3\ \mathrm{jobs}}{40\ \mathrm{days}}

    So in one day, the helper can complete 3/40ths of a job. To find the number of days it would take to complete an entire job, take the reciprocal:

    1\ \mathrm{job}\cdot\frac{40\ \mathrm{days}}{3\ \mathrm{jobs}}=13.\overline{3}\ \mathrm{ days}.
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  3. #3
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    Re: Calculating Work Done.

    Really great, very nicely solved by Reckoner, even i got agreed with solution. Thanks for solving this problem.
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