SOLUTION: A swimming pool can be filled using the inlet pipe and emptied with the drain pipe. It takes 3 hours less to fill the pool using just the inlet pipe than to empty the pool with onl

Question 1154141: A swimming pool can be filled using the inlet pipe and emptied with the drain pipe. It takes 3 hours less to fill the pool using just the inlet pipe than to empty the pool with only the drain pipe. While filling the pool with the drain pipe open, the owner realized it takes 12 more hours than filling the pool using just the inlet pipe. How much time does it take to fill the pool using just the inlet pipe?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
A swimming pool can be filled using the inlet pipe and emptied with the drain pipe. It takes 3 hours less to fill the pool using just the inlet pipe than to empty the pool with only the drain pipe. While filling the pool with the drain pipe open, the owner realized it takes 12 more hours than filling the pool using just the inlet pipe. How much time does it take to fill the pool using just the inlet pipe?
Let it take x hours to drain the pool
It drains 1/x of the pool in 1 hour.
It takes (x-3) hours to fill the pool only with inlet on
The pipe fills 1/(x-3) of the pool in one hour.
When both are open it takes (x-3)+12 hours = x+9 hours
Thus 1/(x+9) of the pool is filled in 1 hour

Simplify
3/x(x-3) = 1/(x+9)
3(x+9) = x(x-3)
3x+27 = x^2-3x
x^2 -6x -27=0
(x-9)(x+3)=0
x=9
Alone the pipe takes 6 hours to fill the pool. (x-3)

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