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intermediate algebra

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Dal and Kim can assemble a swing set in 1/1/2 hrs,working alone it takes Kim 4 hrs longer than Dal to assemble the swing set.How long would it take Dal to working alone to assemble the set

  • intermediate algebra -

    Dal takes d
    Kim takes k
    Dal&Kim take b (for both)

    1/b = 1/d + 1/k
    1/(3/2) = 1/d + 1/(d+4)

    2/3 = 1/d + 1/(d+4)
    multiply through by 3d(d+4) to get
    2d(d+4) = 3(d+4) + 3d
    2d^2 + 8d = 3d + 12 + 3d
    2d^2 + 2d - 12 = 0
    d^2 + d - 6 = 0
    (d+3)(d-2) = 0

    d = -3 or 2

    must have positive time, so d=2

    That is, Dal takes 2 hours by himself

    check:
    1/2 + 1/6 = 2/3 = 1/(3/2)

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