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15 September, 05:28

Bill can paint a small house in 3 days, Sharon can paint a small house in 4 days and Wilber can paint a small house in 5 days. How long will it take for Bill, Sharon and Wilber together to paint one small house? Give your answer a fraction.

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  1. 15 September, 07:36
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    To solve this problem, let us say that the action of totally painting a small house is called "1 job". Therefore the rates of each person in painting the small house are:

    Bill = 1 job / 3 days = 1 / 3

    Sharon = 1 job / 4 days = 1 / 4

    Wilber = 1 job / 5 days = 1 / 5

    Therefore the total rate is calculated by simply adding the rates of the three.

    (1 / 3) + (1 / 4) + (1 / 5) = 1 / x

    where x is the number of hours it take if all them paint together

    Calculating for by multiplying both sides by 60:

    60 [ (1 / 3) + (1 / 4) + (1 / 5) = 1 / x]

    (60/3) + (60/4) + (60/5) = 60 / x

    20 + 15 + 12 = 60 / x

    47 = 60 / x

    x = 60 / 47 hours

    Answer:

    60/47 hours
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