SOLUTION: It takes 24 minutes for Peter and John to mow the lawn together. If Peter mows 20 minutes faster than John. How long will it take each man working alone to mow the lawn?

Question 205962: It takes 24 minutes for Peter and John to mow the lawn together. If Peter mows 20 minutes faster than John. How long will it take each man working alone to mow the lawn?

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
It takes 24 minutes for Peter and John to mow the lawn together. If Peter mows 20 minutes faster than John. How long will it take each man working alone to mow the lawn?
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If by "Peter mows 20 minutes faster than John" you mean it takes Peter 20 minutes less to do the job:
It takes Peter x minutes
It takes John x+20 minutes
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Peter does 1/x of the job per minute
John does 1/(x+20) of the job per minute
Together, they do 1/x + 1/(x+20) per minute which is 1/24 of the job.
1/x + 1/(x+20) = ((x+20) + x)/(x*(x+20)) = 1/24
1/24 = (2x+20)/(x^2+20x)
24 = (x^2+20x)/(2x+20)
24(2x+20) = x^2+20x
48x+480 = x^2+20x
x^2 - 28x - 480 = 0
(x-40)*(x+12) = 0
x = 40 minutes (Ignore the -12)
It takes Peter 40 minutes
It takes John 60 minutes.
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Check with product over sum
40*60/(40+60) = 2400/100 = 24 minutes.

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