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Question 921772: Working together, Verna and Sam can paint their living room in 2 hours. Working alone, it would take Sam 3 hours longer than Verna to paint the living room. How long would it take Verna to paint the living room working by herself?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Working together, Verna and Sam can paint their living room in 2 hours. Working alone, it would take Sam 3 hours longer than Verna to paint the living room. How long would it take Verna to paint the living room working by herself?
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Together rate:: 1/2 job/hr
Verna rate:: 1/x job/hr
Sam rate:: 1/(x+3) job/hr
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Equation:
rate + rate = together rate
1/x + 1/(x+3) = 1/2
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2(x+3) + 2x = x(x+3)
4x + 6 = x^2 + 3x
x^2 - x - 6 = 0
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Factor:
(x-3)(x+2) = 0
Positive solution::
x = 3 (Verna's time to do the job alone)
x+3 = 6 (Sam's time to do the job alone)
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Cheers,
Stan H.
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