Question 706228
In other words, every 3 hours, the 1st pipe fills for 2 hours
and the 2nd pipe empties for 1 hour.
Let {{{ 3t }}} = time in hours to fill the tank
{{{ 2t }}} will be the 1st pipe's time filling
{{{ t }}} will be the 2nd pipe's time emptying
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( 1 tank ) / ( 12 hrs ), or {{{ 1/12 }}} is the 1st pipe's rate
( 1 tank ) / ( 24 hrs ) or {{{ 1/24 }}} is the 2nd pipe's rate
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Note that (rate)x(time) = fraction of tank filled or emptied
{{{ (1/12)*2t - (1/24)*t = 1 }}}
This says ( fraction of tank filled ) - ( fraction emptied ) = ( 1 tank filled )
Divide both sides by {{{ t }}}
{{{ 2/12 - 1/24 = 1/t }}}
{{{ 4/24 - 1/24 = 1/t }}}
{{{ 3/24 = 1/t }}}
{{{ 1/8 = 1/t }}}
{{{ t = 8 }}}
{{{ 3t = 24 }}}
It will take 24 hrs to fill the tank