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 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

{{{1/X-1/(X+6) = 1/120}}}


LCM = X(X+6)


{{{(X+6-X)/X(X+6) = 1/120}}}


{{{6/(X^2+6X) = 1/120}}}


On cross-multiplying, we get....

{{{X^2+6X = 720}}}

{{{X^2+6X-720 = 0}}}

Solving the quadratic equation by splitting the middle term

{{{X^2-24X+30X-720 = 0}}} 
  
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