Question 1098908
[ liters in pool ] / [ liters/min filling rate ] = [ min to fill pool ]
{{{ 4000 / 20 = 200 }}} min filling time
The pool fills in 200 min
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[ liters/min ] x { min ] = [  liters ] 
{{{ 20*20 = 400 }}} liters put into  pool after 20 min
{{{ 4000 - 400 = 3600 }}} liters left in pool
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Let {{{ t }}} = the elapsed time in minutes after 20 min 
during which pool both fills and empties until it is full
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Time to empty 1 pool at 2 liters/min:
{{{ 4000/2 = 2000 }}} min
Add rates to get final rate of filling:
[ 1 pool / 200 min ]  - [ 1 pool emptied / 2000 min ] = [ 9/10 pool filled / t min ]
{{{ 1/200 - 1/2000 = (( 3600/4000 ))/t }}}
{{{ 1/200 - 1/2000 = 9/( 10t ) }}}
Multiply both sides by {{{ 2000t }}}
{{{ 10t - t = 1800 }}}
{{{ 9t = 1800 }}}
{{{ t = 200 }}} min
Now add in the initial 20 min
This is 220 min to fill the pool
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Definitely feel free to get another opinion ( if needed )