SOLUTION: A swimming pool is filled through its inplet pipe and then emptied through its outlet pipe in a total of 8 hours. If water enters through its inlet and simultaneously allowed to le

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Question 997137: A swimming pool is filled through its inplet pipe and then emptied through its outlet pipe in a total of 8 hours. If water enters through its inlet and simultaneously allowed to leave through its outlet, the pool is filled in 7.50 hours. Find how long will it take to fill the pool wih the outlet closed.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
1 POOL, the unit of volume
Oultet at the rate 1/x
Inlet at the rate 1/y
t, time used in filling 1 pool in the step-wise process described

Filling and Emptying in 8 hours
          rate       time     quantity
FILL      1/y         t        (1/y)t
EMPTY     1/x        8-t       (1/x)(8-t)
Total                 8         1

This gives an equation %281%2Fy%29t-%281%2Fx%29%288-t%29=1.

The fill process with BOTH pipes open gives %281%2Fy-1%2Fx%29=1%2F7.5 and the best you might do is to solve for 1%2Fx and substitute into the step-wise equation; but you will still have the UNKNOWN variables of t and y.

Your problem description seem incomplete. No finished answer. Maybe another tutor will see a better way.

--
-1%2Fx=1%2F7.5-1%2Fy
1%2Fx=1%2Fy-1%2F7.5
-
%281%2Fy%29t-%281%2Fy-1%2F7.5%29%288-t%29=1
%281%2Fy%29t%2B%281%2F7.5-1%2Fy%29%288-t%29=1
%281%2Fy%29t%2B8%2F7.5-%281%2Fy%298-t%2F7.5%2Bt%2Fy=1
%281%2Fy%29t%2B8%2F7.5-8%2Fy-t%2F7.5%2Bt%2Fy=1, LCD 7.5y;
7.5t%2B8y-8%287.5%29-t%2Ay%2B7.5t=1
15t%2B8y-ty-60=1----------still the two unknowns y and t.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A swimming pool is filled through its inplet pipe and then emptied through its outlet pipe in a total of 8 hours. If water enters through its inlet and simultaneously allowed to leave through its outlet, the pool is filled in 7.50 hours. Find how long will it take to fill the pool wih the outlet closed. 
Time inlet pipe takes to fill pool = highlight_green%283%29 hours