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Question 611352: A 400-gallon water storage tank is filled by a single inlet pipe, and two identical outlet pipes can be used to supply water to the surrounding fields (see the figure). It takes 4 hours to fill an empty tank when both outlet pipes are open. When one outlet pipe is closed, it takes 3 hours to fill the tank. Find the flow rates (in gallons per hours) in and out of the pipes.
Inlet?
Outlet?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A 400-gallon water storage tank is filled by a single inlet pipe, and two identical outlet pipes can be used to supply water to the surrounding fields (see the figure). It takes 4 hours to fill an empty tank when both outlet pipes are open. When one outlet pipe is closed, it takes 3 hours to fill the tank. Find the flow rates (in gallons per hours) in and out of the pipes.
Inlet?
Outlet?
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Let i by the rate of the inlet pipe.
Let t be the rate of one of the outlet pipes.
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Equation:
i - 2t = 1/4
i - t = 1/3
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Subtract and solve for "t":
t = (1/3-(1/4)
t = 1/12 job/hr (flow rate of each of the outlet pipes)
Each outlet pipe removes 400/12 = 33 1/3 gallons per hour
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Solve for "i":
i - t = 1/3
i = 1/12 + 1/3
i = 15/36 = 5/12 job/hr (flow rate of the input pipe)
The input pipe feeds (5/12)400 = 166 2/3 gallons per hour.
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Cheers,
Stan H.
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