Question 956567
The rate of filling of the 1st pipe is:
[ 1 tank filled ] / [ 3 hrs ]
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The rate of emptying of the 2nd pipe is:
-[ 1 tank emptied ] / [ 6 hrs ]
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Notice that the emptying rate has to have
a minus sign to make it opposite the
filling rate
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Let {{{ 1/t }}} = the rate of filling with
both pipes open
Add the rates to get the rate working together
{{{ 1/3 - 1/6 = 1/t }}}
Multiply both sides by {{{ 6t }}}
{{{ 2t - t = 6 }}}
{{{ t = 6 }}}
It will take 6 hrs to fill the tank
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This makes sense because in 6 hrs, the 1st pipe
fills the tank twice
In that same 6 hrs, the 2nd pipe empties the
tank once
and you are left with 1 tank full