SOLUTION: Hi, having difficulty with a problem in math. When a drain is closed, a swimming pool can be filled in 4 hours. When the drain is opened it takes 5 hours to empty the pool. The p

Question 640140: Hi, having difficulty with a problem in math.
When a drain is closed, a swimming pool can be filled in 4 hours. When the drain is opened it takes 5 hours to empty the pool. The pool is being filled, but the drain was accidently left open. How long until the pool is filled?
Found 2 solutions by lwsshak3, DrBeeee:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
When a drain is closed, a swimming pool can be filled in 4 hours. When the drain is opened it takes 5 hours to empty the pool. The pool is being filled, but the drain was accidently left open. How long until the pool is filled?
**
let x=time it takes to fill the pool
fill rate=1/4
drain rate=1/5
..
x/4-x/5=1
5x-4x=20
x=20
time it takes to fill the pool=20 hrs
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let G = the capacity of the pool.
Let r = fill rate in gallons/hour
Let d = drain rate in gallons/hour
Then G = rate*time, where time is hours.
From the first statement, we fill the pool in 4 hours, we have
(1) G = r*4
And drain statement we have
(2) G = d*5
When we fill with the drain open the net fill rate is
(3) net rate = (r-d) gal/hr
Let T = the time to fill with the drain open, then we have
(4) G = (r-d)*T
Substitute (1) and (2) into (4) yields
(5) G = (G/4 - G/5)*T
Note that G cancels, giving
T = 1/(1/4 - 1/5) or
T = 1/((5-4)/20) or
(6) T = 20
Answer: When the drain is open, it will take 20 hours to fill the pool.

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