A 300 gallon water storage tank is filled by a single intlet

A 300 gallon water storage tank is filled by a single intlet pipe, and two identical outlet pipes can be used to supply water to the surrounding fields. It takes 5 hours to fill and empty tank when both outlet pipes are open. It takes 3 hours to fill the tank when only one outlet pipe is closed. Find the flow rates (in gallons per hour) of the inlet and outlet pipe.

Solution

Let the flow rate of one outlet pipe be x gallons/hour. Then the flow rate of both the ioutet pipes is 2x gallons/hour. Let us assume that the flow rate of the single inlet pipe is y gallons per hour. Since It takes 5 hours to fill the tank when both outlet pipes are open, we have 5(y - 2x) = 300 or, y - 2x = 60...(1). Also, since it takes 3 hours to fill the tank when only one outlet pipe is open, we have 3(y - x) = 300 or, y -x = 100...(2). On subtracting the 1st equation from the 2nd equation, we have y - x - y + 2x = 100 - 60 or, x = 40. THen, on substituting x = 40 in the 2nd equation, we have y - 40 = 100 so that y = 100 + 40 = 140. We can verify this result by substituting x = 40 and y = 140 in the 1st equation,. On substitution, we have 140 - 2*40 = 60 or, 140 -80 = 60 which is correct. Therefore, the flow rates (in gallons per hour) of the inlet and each outlet pipes are 140 and 40 respectively.