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college algebra

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a mason can build a wall in 6 hours less than an apprentice. Together they can build the wall in 4 hours. How long would it take the apprentice to build the wall?

  • college algebra - ,

    time for apprentice -- x
    time for mason -- x-6

    rate of apprentice = 1/x
    rate of mason = 1/(x-6)
    combined rate = 1l/x + 1/(x-6)
    = (2x - 6)/(x(x-6))

    then

    1/[(2x - 6)/(x(x-6))] = 4
    x(x-6)/2x-6) = 4
    x^2 - 6x = 8x - 24
    x^2 - 14x + 24=0
    (x-12)(x-2) = 0
    x = 12 or x = 2 , the last makes no sense since x-6 would be negative

    so x = 12
    the apprentice could build the wall in 12 hours

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