SOLUTION: A swimming pool holds 600 cubic meters of water. It can be drained at the rate of 9 minutes faster than it can be filled. If it takes half an hour to fill it than to drain it, find

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Question 241501: A swimming pool holds 600 cubic meters of water. It can be drained at the rate of 9 minutes faster than it can be filled. If it takes half an hour to fill it than to drain it, find the drainage rate.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A swimming pool holds 600 cubic meters of water.
It can be drained at the rate of 9 minutes faster than it can be filled.
If it takes half an hour to fill it than to drain it, find the drainage rate.
:
I couldn't make any sense of this problems until I add "gal/min" so it reads:
:
A swimming pool holds 600 cubic meters of water.
It can be drained at the rate of 9 gal/min faster than it can be filled.
If it takes a half an hour more to fill it than to drain it, find the drainage rate.
:
Let r = rate in gal/min to drain it
then
(r-9) = rate in gal/min to fill it
:
Fill time - drain time = half-hour
600%2F%28r-9%29 - 600%2Fr = 30 min
Multiply equation by r(r-9), results
600r - 600(r-9) = 30r(r-9)
:
600r - 600r + 5400 = 30r^2 - 270r
Arrange as quadratic equation
30r^2 - 270r - 5400 = 0
Simplify, divide by 30
r^2 - 9r - 180 = 0
:
Use the quadratic formula to find r: a=1; b=-9; c= -180
:
The positive solution
r = 18.651 gal/min to drain it
;
;
Check solution
600%2F9.651 - 600%2F18.651 =
62.17 - 32.17 = 30 minutes