Question 436132
.
Word problem.

It takes 60 minutes to fill a pond with water alone.
It takes 80 minutes to drain a pond of water alone.

How long will it take to fill the pond while it is being drained at the same time?
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        The solution in the post by @mananth is  FATALLY  WRONG  due to elementary arithmetic error.

        I came to bring a correct solution.



consider filling or emptying the pool as 1 job.

emptying the pool = 80 minutes
so 1/80 of the job is done in 1 minute
...
Filling time = 60 minutes
1/60 of the job in 1 minute
..
difference = 1/60 -1/80
(80-60)/80*60
20/4800
1/240 of the job is done in 1 minute when both are on.

so it will take 240 minutes = 4 hours to fill the pool.


Solved correctly.



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It can be seen even with unarmed eye, using common sense - ONLY.


The filling hose fills the tank in 1 hour - but then the drain takes out 3/4 of the water 
from the tank during this 1 hour,
so only 1/4 of the tank is filled in one hour.


Hence, 4 hours are needed.