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math

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john takes 3hours longer than andrew to peel 400 pounds of apples. if together they can peel 400pounds of apples in 8hours then how long would it take john if he is working alone.

  • math -

    Andrew's rate = 400/x
    Johns rate = 400/(x+3)
    combined rate = (400(x+3) + 400x)/(x(x+3)
    = 400(2x+2)/(x(x+2))

    400 / [400(2x+3)/(x(x+3) ] = 8
    1/[2x+3)/(x(x+2)) ] = 8
    x(x+3)/(2x+3) = 8
    x^2+3x = 16x + 24
    x^2 - 13x - 24 = 0

    x = (13 ±√265)/2
    x = 14.64 hrs , ignoring the negative answer


    check:
    combined rate = 1/14.64 + 1/17.64 = .125
    time at comined time = 1/.125 = 8 , Yeahh!

    Andrew alone can do it in 14.65 hrs
    John alone can do it in 17.65 hrs

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