SOLUTION: An elevated concrete tank is filled through its inlet pipe and then is emptied through its outlet pipe in a total time of 9 hours. If water enters through the inlet pipe and i
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Question 1196842: An elevated concrete tank is filled through its inlet pipe and then is emptied through its outlet pipe in a total time of 9 hours. If water enters through the inlet pipe and is simultaneously allowed to leave through the outlet pipe, the tank is filled in 20 hours. How long will it take to fill the tank if the outlet is closed? Answer by greenestamps(13200) (Show Source):
let x = # of hours to fill the tank; then 1/x is the fraction of the tank that is filled in 1 hour
let y = # of hours to drain the tank; then 1/y is the fraction of the tank that is drained in 1 hour
The tank is filled and then drained in 9 hours, so
(1)
When the tank is being drained at the same time it is being filled, the fraction of the tank that gets filled in 1 hour is 1/x - 1/y. In that situation, the tank gets filled in 20 hours, so 1/20 of the tank is getting filled each hour:
(2)
There are two equations in x and y that you can solve by many different methods. Perhaps this....
Multiply through by the least common multiple of the denominators, which is :
The time to fill the tank is either 45 hours or 4 hours -- but the 45 hours is not consistent with the given information. So
ANSWER: The number of hours to fill the tank with the drain closed is x = 4
Note that is a lot of ugly algebra to solve a problem that can be solved mentally by playing with numbers a bit:
