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math

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working together 2 people can mow a large lawn in 4 hours. One person can do the job alone one hour faster than the other person. How long does it take each person working alone to mow the lawn?

  • math -

    rate of faster person = 1/x
    rate of slower person = 1/(x+1)

    combined rate = 1/x + 1/(x+1) = (2x+1)/(x(x+1))

    so time with combined rate = 1/[(2x+1)/(x(x+1))
    = x(x+1)/(2x+1)

    so x(x+1)/(2x+1) = 4
    x^2 + x = 8x + 4
    x^2 - 7x -4 = 0
    x = (7 ± √ 65)/2
    = 7.53 or a negatiave

    So one takes 7.53 hours, the other 8.53 hours

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