Question 904583
Rate of filling:
( 1 tank ) / ( 10 min )
Rate of emptying:
( 1 tank ) / ( 20 min )
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Add the rates:
( minus sign means pipe empties )
{{{ 1/10 - 1/20 = 1/t }}}
Multiply both sides by {{{ 20t }}}
{{{ 2t - t = 20 }}}
{{{ t = 20 }}}
After 20 min, the tank overflows
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check:
Let {{{ x }}} = volume of tank filled
( 1 = tank filled )
{{{ 1/10 - 1/20 = x/20.1 }}}
( {{{ 20.1 }}} min have passed )
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{{{ 2/20 - 1/20 = x/20.1 }}}
{{{ 1/20 = x/20.1 }}}
{{{ 20.1 = 20x }}}
{{{ x = 1.005 }}}
( tank starts to overflow )