SOLUTION: Karen and John take 3 hours to clean the house. Karen alone can clean the house 1 hour faster than John can clean the house alone. What is the total time it takes Karen to clean
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Question 65067: Karen and John take 3 hours to clean the house. Karen alone can clean the house 1 hour faster than John can clean the house alone. What is the total time it takes Karen to clean the house alone.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Karen and John take 3 hours to clean the house. Karen alone can clean the house 1 hour faster than John can clean the house alone. What is the total time it takes Karen to clean the house alone.
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Karen/John together DATA:
time=3 hrs/job; rate=(1/3)job/hr.
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John alone DATA:
time= x hrs/job; rate = (1/x)job/hr.
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Karen alone DATA:
time = (x+1) hr/job ; rate = 1/(x+1) job/hr
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EQUATION:
rate + rate = rate together
(1/x)+1/(x+1)= 1/3
Multiply thru by 3x(x+1) to get:
3(x+1)+3x = x(x+1)
6x+3=x^2+x
x^2-5x-3=0
x=[5+-sqrt(25-4*-3)]/2
x=[5+-sqrt(37)]/2
x= 5.541 hrs
x+1=6.541 hrs (Time it takes Karen alone to clean the house)
Cheers,
Stan H.
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