Question 941794
Rate of emptying:
( 1 tub ) / ( 10 min )
Rate of filling with plug in:
( 1 tub ) / ( 8 min )
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What you have to realize at this point is
that the rate of filling is greater than the
rate of emptying, so if you pull the plug
out, the tub will EVENTUALLY fill up.
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Let {{{ t }}} = the time in minutes for the tub
to fill if the tap is on and the plug is removed
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Add the rate of filling
Subtract the rate of emptying
Make that equal to:
( 1 tub filled ) / ( t min ) = {{{ 1/t }}}
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{{{ 1/8 - 1/10 = 1/t }}}
Multiply both sides by {{{ 40t }}}
{{{ 5t - 4t = 40 }}}
{{{ t = 40 }}}
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In 40 min the tub will fill if the tap is 
on and the plug is removed
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check:
{{{ 1/8 - 1/10 = 1/40 }}}
{{{ 5/40 - 4/40 = 1/40 }}}
{{{ 1/40 = 1/40 }}}
OK