SOLUTION: A swimming pool is 15ft by 30ft and an average of 5ft in depth. It takes 25 minutes longer to fill than to drain the pool. If it can be drained at a rate of 15ft(cubed)/min faster

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)