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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