SOLUTION: Peter takes 15 minutes longer to mow the lawn by himself than charles dows. Together they mow the lawn in 18 minutes. How long does it take for charles to mow the lawn by himselves

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Question 101041: Peter takes 15 minutes longer to mow the lawn by himself than charles dows. Together they mow the lawn in 18 minutes. How long does it take for charles to mow the lawn by himselves?

I am having trouble figruing out the equasion of this problem.
I DO KNOW THIS:
p= c+15
c+p=18
p=c+15
c+p=18
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Peter takes 15 minutes longer to mow the lawn by himself than charles dows. Together they mow the lawn in 18 minutes. How long does it take for charles to mow the lawn by himself?
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Charles DATA:
time = x minutes/job ; rate = 1/x job/min
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Peter DATA;
time = x+15 min/job ; rate = 1/(x+15) job/min
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Together DATA:
time = 18 min/j job ; rate = 1/18 job/min
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EQUATION:
rate + rate = together rate
1/x + 1/(x+15) = 1/18
Multiply thru by 18x(x+15)
18(x+15) + 18x = x(x+18)
18x+18*15 + 18x = x^2 + 18x
x^2 -18x -270 = 0
x = [18 +- sqrt(18^2-4*-270)]/2
x = [18 +- 37.47]/2
Positive answer:
x = 27.735 minutes (time for Charles to do the job)
x+15 = 42.735 (time for Peter to do the job)
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Cheers,
Stan H.