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A father and his son can clean the house together in 7 hours. When the son works alone, it takes him an hour longer to clean than it takes his dad alone. Find how long it takes the son to clean alone

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2 answers

  1. Dad's rate = 1/d
    son's rate = 1/s
    combined rate = (s+d)/(sd)
    1/((s+d)/sd) = 7
    sd/(s+d) = 7
    7s + 7d = sd

    1/(1/s) - 1/(1/d) = 1
    s - d = 1 or s = 1+d

    sub into the other equation
    7(1+d) + 7d = d(1+d)
    14d + 7 = d + d^2
    d^2 - 13d -7 = 0
    d = 13.52 hrs
    s = 14.52 hrs <------ answer

    check: combined rare = (13.52+14.52)/(13.52*14.52) = .1428..
    time at combined rate = 1/.1428... = 7

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  2. 1/s + 1/(s-1) = 1/7
    s = 14.52

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