SOLUTION: A swimming pool is 15 ft by 30 ft by 5 ft. It takes 25 minutes longer to fill than to drain the pool. It can be drained at a rate of 15ft cubed per minute faster than it can be fil

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Question 394161: A swimming pool is 15 ft by 30 ft by 5 ft. It takes 25 minutes longer to fill than to drain the pool. It can be drained at a rate of 15ft cubed per minute faster than it can be filled, what is the drainage rate?
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi, Note**
V(pool) = 15*30*5 ft^3 = 2250 ft^3
**drained at a rate of 15ft cubed per minute faster than it can be filled
Let x and (x+15)represent the fill and drainage rates respectively
Question States: t(drain) = 2250 ft^3/(x+15)
t(fill) = 2250 ft^3/(x+15) + 25 = 2250/x |takes 25 minutes longer to fill
2250 ft^3/(x+15) + 25 = 2250/x
2250x + 25x(x+15) = 2250(x+15)
25x^2 + 375x - 33750 = 0
x^2 +15 - 1350 =0
factoring
(x +45)(x-30)=0
(x +45)= 0 tossing out negative solution
(x-30)=0 x = 30 ft^3/min, fill rate. Drainage rate is 45 ft^2/min (30+15)
CHECKING our Answer
t(drain)=2250/45 = 50min t(fill)= 2250/30 = 75min (25min longer)


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