Question 134367: The O'Connors own a small janitorial service. John requires 3/4 hour more time to clean the Moose club by himself than Chris does working by herself. If together they can clean the club in 6 hours, find the time required by each to clean the club.
The time it takes Chris is about ? hours. Round to two decimal places as needed.
The time it takes John is about ? hours. Round to two decimal places as needed.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The O'Connors own a small janitorial service. John requires 3/4 hour more time to clean the Moose club by himself than Chris does working by herself. If together they can clean the club in 6 hours, find the time required by each to clean the club.
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Chris DATA:
Time = x hr/job ; Rate = 1/x job/hr
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John DATA:
time = (x+(3/4))= [(4x+3)/4] hr/job ; Rate = [4/(4x+3)] job/hr
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Together DATA:
Time = 6 hr/job ; Rate = 1/6 job/hr
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EQUATION:
rate + rate = together rate
1/x + 4/(4x+3) = 1/6
Multiply thru by 6x(4x+3) to get:
6(4x+3) + 4x*6 = x(4x+3)
24x+18 + 24x = 4x^2+3x
4x^2-45x-18 = 0
x = [45 +- sqrt(45^2-4*4*-18)]/8
x = [45 +- sqrt(2313)]/8
x = [45 +- 48.09]/8
Positive solution:
x = 11.64 hrs (Time Chris requires to clean the club)
x+(3/4) = 12.39 hrs (Time John requires to clean the club)
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Cheers,
Stan H.
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