SOLUTION: When a large pipe and a small pipe are opened for 4 hours and 9 hours respectively, a tank is half filled. But when both pipes are opened simultaneously the tank is filled in 12 ho

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Question 940761: When a large pipe and a small pipe are opened for 4 hours and 9 hours respectively, a tank is half filled. But when both pipes are opened simultaneously the tank is filled in 12 hours. How many hours does the larger pipe take to fill the tank?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
When a large pipe and a small pipe are opened for 4 hours and 9 hours respectively, a tank is half filled. But when both pipes are opened simultaneously the tank is filled in 12 hours. How many hours does the larger pipe take to fill the tank?
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Equation:
4(1/L) + 9(1/S) = 1/2
8(1/L) + 18(1/S) = 1 job
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Together DATA:
time = 12 hrs ; rate = 1/12 job/hr
(1/L) + 1/(S) = 1/12 job
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Solve the System of equations::
(8/L) + 18/S = 1
(1/L) + (1/S) = 1/12
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(8/L) + (18/S) = 1
(8/L) + 8/S) = 8/12
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Subtract and solve for "S
10/S = 4/12
S = 120/4 = 30 hrs (time for the smaller to fill the tank alone)
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Solve for "L"::
(1/L) + 1/30 = 1/12
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1/L = (1/12)-(1/30)
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1/L = (30-12)/12*30
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1/L = 18/(12*30) =
L = 20 hrs (time for the larger pipe to fill the tank alone)
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Cheers,
Stan H.
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