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Question 183281: Two pipes can be used to fill a pool. Working together, the two pipes can fill the pool in 2 hours. The larger pipe can fill the pool in 4 hours less time than the smaller pipe can alone. Find the time to the nearest tenth of an hour it takes for the smaller pipe working alone to fill the pool.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Two pipes can be used to fill a pool. Working together, the two pipes can fill the pool in 2 hours. The larger pipe can fill the pool in 4 hours less time than the smaller pipe can alone. Find the time to the nearest tenth of an hour it takes for the smaller pipe working alone to fill the pool.
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Together DATA:
time = 2 hrs/job ; rate = 1/2 job/hr
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Larger pipe DATA:
time = x-4 hrs/job ; rate = 1/(x-4) job/hr
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Smaller pipe DATA:
time = x hrs/job ; rate = 1/x job/hr.
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Equation:
rate + rate = together rate
1/x + 1/(x-4) = 1/2
Multiply thru by 2x(x-4) to get:
2(x-4) + 2x = x(x-4)
4x - 8 = x^2 - 4x
x^2 - 8x + 8 = 0
x = [8 +- sqrt(64 - 4*1*8)]/2
Positive solution:
x = [8 + sqrt(32)]/2
x = [4 + 2sqrt(2)] = 6.8 minutes
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Cheers,
Stan H.
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