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Math Help - SAT Work Problem

  1. #1
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    SAT Work Problem

    I can't seem to figure out the following problem and how to set it up:

    Paul and Mary can do a job in 2 hours. When Paul works alone, he can do 5 jobs in 15 hours. How many jobs can Mary do in 12 hour, alone?

    The answer in the SAT book says 2 jobs.

    Thanks.
    Last edited by Tracer; August 3rd 2010 at 01:20 PM. Reason: Added a line.
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by Tracer View Post
    I can't seem to figure out the following problem and how to set it up:

    Paul and Mary can do a job in 2 hours. When Paul works alone, he can do 5 jobs in 15 hours. How many jobs can Mary do in 12 hour, alone?

    The answer in the SAT book says 2 jobs.

    Thanks.
    It might help if you write units everwhere, and the units will tell you what needs to be multiplied with what

    let P = Paul's rate, which will be jobs/hour
    let M = Mary's rate, which will be jobs/hour

    So P+M = 1/2 jobs/hour

    P = 5/15 = 1/3 jobs/hour

    So M = 1/2 - 1/3 = 1/6 jobs/hour

    So in 12 hours, Mary can do 2 jobs. (If you want to write explicitly, multiply 12 hours by 1/6 jobs/hour).
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  3. #3
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    Hello, Tracer!

    Paul and Mary can do a job in 2 hours.
    When Paul works alone, he can do 5 jobs in 15 hours.
    How many jobs can Mary do in 12 hour, alone?

    We are told: Paul can do 5 jobs in 15 hours.
    . . Hence, he can do 1 job in 3 hours.
    In one hour, Paul can do \frac{1}{3} of a job.

    Let M = number of hours for Mary to do a job alone.
    In one hour, she can do \frac{1}{M} of the job.

    Working together for one hour, they can do: . \frac{1}{3} + \frac{1}{M} of the job. .[1]


    Working together, they can do the job in 2 hours.
    Working together for one hour, they can do \frac{1}{2} of the job. .[2]


    Note that [1] and [2] both describe the same quantity.

    There is our equation! . . . . \dfrac{1}{3} + \dfrac{1}{M} \:=\:\dfrac{1}{2}


    Multiply by 6M\!:\;\;2M + 6 \:=\:3M \quad\Rightarrow\quad M \:=\:6


    Hence. Mary takes 6 hours to do a job alone.

    Therefore, in 12 hours she can do 2 jobs.



    Edit: I was too slow again . . .
    . . . .This is a slight variation of undefined's solution.
    .
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