SOLUTION: alone. How long would it take each of them to paint the house alone?A man and his son working together can paint their house in 4 days. The man can do the job alone in 6 days less

Question 113308: alone. How long would it take each of them to paint the house alone?A man and his son working together can paint their house in 4 days. The man can do the job alone in 6 days less than it takes the son
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A man and his son working together can paint their house in 4 days. The man can do the job alone in 6 days less than it takes the son alone. How long would it take each of them to paint the house alone?
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Together DATA:
Time = 4 days/job ; Rate = 1/4 job/day
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Son DATA:
Time = x days/job ; Rate = 1/x job/day
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Father DATA:
Time = x-6 days/job ; Rate = 1/(x-6) job/day
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EQUATION:
rate + rate = together rate
1/x + 1/(x-6) = 1/4
Multiply thru by 4x(x-6) to get:
4(x-6) + 4x = x(x-6)
4x-24 + 4x = x^2-6x
x^2-14x+24 = 0
(x-2)(x-12)=0
x = 2 or x=12
Realistic answer is x=12
Son's Time = 12 days to do the job
Father's Time ; x-6 = 6 days to do the job.
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Cheers,
Stan H.

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