SOLUTION: Wendy and Maddy, working together can paint a house in 6 days. Wendy by herself can complete this job in 5 days less than Maddy. How Long will it take Wendy to complete the job by

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Question 288813: Wendy and Maddy, working together can paint a house in 6 days. Wendy by herself can complete this job in 5 days less than Maddy. How Long will it take Wendy to complete the job by herself?
Answer by stanbon(75887) (Show Source):
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Wendy and Maddy, working together can paint a house in 6 days. Wendy by herself can complete this job in 5 days less than Maddy. How Long will it take Wendy to complete the job by herself?
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Together time = 6 days/job ; rate = 1/6 job/day
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Maddy time = x days/job ; rate = 1/x job/day
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Wendy time = x-5 day/job ; rate = 1/(x-5) job/day
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Equation:
rate + rate = together rate
1/x + 1/(x-5) = 1/6
Multiply thru by 6x(x-5)
6(x-5) + 6x = x(x-5)
6x-30 + 6x = x^2-5x
x^2 -17x + 30 = 0
Factor:
(x-2)(x-15) = 0
Realistic Solution:
x = 15 hrs (Maddy's time to do the job alone)
x-5 = 10 hrs (Wendy's time to do the job alone)
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Cheers,
Stan H.