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Math Help - A "work" word problem, need help!

  1. #1
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    A "work" word problem, need help!

    This problem is driving me nuts, help would be greatly appreciated.


    "One person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together?"


    If they worked at the same time, i know the answer is just under 5 hours total...but the first person has to work 2 hours less, and i dont know how to insert that in.

    Any ideas? thanks!
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  2. #2
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    Quote Originally Posted by itokai View Post
    This problem is driving me nuts, help would be greatly appreciated.


    "One person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together?"


    If they worked at the same time, i know the answer is just under 5 hours total...but the first person has to work 2 hours less, and i dont know how to insert that in.

    Any ideas? thanks!
    Let W denote the total amount of work which should be done. Then the first person is doing \frac W8 per hour and the second person is doing \frac W{12} per hour.

    Let t denote the working time (in hours!) of the second person. Then the first person works only (t - 2) hours. Therefore the complete work is done:

    \frac W8 (t-2) + \frac W{12} t = W

    Divide by W, expand the brackets and collect like terms:

    \frac5{24} t = \frac 54~\implies~\boxed{t = 6\ h}

    Since your question asks "...how many hours will it take them working together?" the answer is 4 hours.
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