Question 394161
  <pre><font size = 3 color = "indigo"><b>
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)