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14 February, 07:58

Mary can make a costume twice as fast as Sam can. If they both work together, they can make it in 6 hours. How long will it take Mary to make the costume if she works alone?

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  1. 14 February, 09:29
    0
    9 hours

    Step-by-step explanation:

    Assume the following:

    Sam's rate = y for the costume

    Mary is twice as fast as Sam; therefore,

    Mary's rate = 2y for the costume

    If Sam and Mary both work together, it will take them 6hours to make the costume.

    Their rate = 1/6

    That is,

    y + 2y = 1/6

    3y = 1/6

    18y = 1

    y = 1/18; taking reciprocal to get time taken = 18 hours

    2y = 2/18

    2y = 1/9 (9 hours (reciprocal)) timetaken by Mary.

    Time taken by Sam = 18 hours

    Time taken by Mary = 9 hours
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