Math

Two painters can paint a room in 2 hours if they work together. The less experienced painter takes 4 hours more than the more experienced painter to finish the job. How long does it take for the less experienced painter to paint the room individually? Round to 2 decimal places.

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  1. rate of faster painter --- 1/x
    rate of slower painter -- 1/(x+4)
    combined rate = 1/x + 1/(x+4)
    = (x+4 + x)/(x(x+4))
    = (2x + 4)/(x^2 + 4)

    1/[(2x + 4)/(x^2 + 4)] = 2
    (x^2 + 4x)/(2x+4) = 2
    x^2 + 4x = 4x + 8
    x^2 = 8
    x = √8 or appr 2.83 hrs

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  2. L = M + 4 ... L - 4 = M

    2/L + 2/M = 1 ... 2M + 2L = L M

    2(2L - 4) = L^2 - 4L ... 0 = L^2 - 8L + 8

    use quadratic formula to find L

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