Question 351547
Rate*Time=Output
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Let {{{Z}}} be the volume of the pool.
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Filling rate: {{{12*R[f]=Z}}}
1. {{{R[f]=Z/12}}}
Draining rate:{{{18*R[d]=Z}}}
2. {{{R[d]=Z/18}}}
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Filling while the drain is open for 12 hrs: {{{(R[f]-R[d])*12=Z1}}}
Find {{{Z1}}}.
Substituting from eq. 1 and eq. 2,
{{{(Z/12-Z/18)*6=Z1}}}
{{{Z1=Z(1/2-1/3)=Z/6}}}
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{{{Z-Z/6=(5/6)Z}}} still needs to be added
Find that time, now the drain has been closed.
{{{R[f]*t=(5/6)Z}}}
{{{(Z/12)*t=(5/6)Z}}}
{{{ t=10 }}} hrs
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Total time:{{{T=12+10}}}
{{{highlight(T=22)}}} hrs