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Question 192860: Working alone, Colleen can paint a house in 2 hr. less than James. Working together, they can paint the house in 8 hours. How long would it take James to paint the house by himself?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Working alone, Colleen can paint a house in 2 hr. less than James. Working together, they can paint the house in 8 hours. How long would it take James to paint the house by himself?
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Colleen DATA:
time = x-2 hrs/job ; rate = 1/(x-2) job/hr.
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James DATA:
time = x hrs/job ; rate = 1/x job/hr.
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Together DATA:
time = 8 hrs/job ; rate = 1/8 job/hr
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Equation:
rate + rate = together rate
1/(x-2) + 1/x = 1/8
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Multiply thru by 8x(x-2)
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8x + 8(x-2) = x(x-2)
8x + 8x-16 = x^2 - 2x
x^2 -18x + 16 = 0
x = [18 +- sqrt(18^2 -4*1*16)]/2
x = [18 +- sqrt(260)]/2
Positive solution:
x = 17.06 hrs (time it would take James to do the job alone)
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Cheers,
Stan H.
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