SOLUTION: it takes 6 hrs longer to empty swimming pool than it does to fill it if you accidentally leave the drain open it wil take 120hrs to fill pool how long would it take if you rememb

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Question 596620: it takes 6 hrs longer to empty swimming pool than it does to fill it
if you accidentally leave the drain open it wil take 120hrs to fill pool
how long would it take if you remember to close the drain.?
Found 2 solutions by lwsshak3, w_parminder:
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
it takes 6 hrs longer to empty swimming pool than it does to fill it
if you accidentally leave the drain open it wil take 120hrs to fill pool
how long would it take if you remember to close the drain.?
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let x=hrs to fill pool with drain closed
work rate: 1/x
x+6= hrs to drain filled pool
work rate: 1/(x+6)
time*fill rate-time*drain rate=1 (100% of pool filled)
120/x-120/(x+6)=1
LCD: x(x+6)
120x+7200-120x=x^2+6x
x^2+6x-7200=0
solve by following quadratic formula:

a=1, b=6, c=-7200
x≈81.91
or
x≈-87.91(reject, x>0)
ans:
If you remember to close the drain, it would take about 82 hours to fill the pool

Answer by w_parminder(53) (Show Source):
You can put this solution on YOUR website!
It takes 6 hrs longer to empty swimming pool than it does to fill it.
If you accidentally leave the drain open it wil take 120hrs to fill the pool.
how long would it take if you remember to close the drain.?

Let time taken to fill the pool(With closed drain) = X hrs
SO rate of Fill = 1/x
Time taken to drain the pool = X + 6 hrs
Rate of Drain = 1/(x+6)
Fill rate - Drain rate = 1/120

LCM = X(X+6)

On cross-multiplying, we get....

Solving the quadratic equation by splitting the middle term

X(X-24) + 30(X-24) = 0
(X-24)(X+30) = 0
This means either (X-24) = 0 OR (X+30) = 0
i.e. X = 24 OR X = -30
But X is the time which can't be negative,
So X = 24
i.e. Time taken to fill the pool(With closed drain) = 24 hrs