Question 350666
Rate*Time=Output
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Let {{{Z}}} be the volume of the pool.
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Filling rate: {{{6*R[f]=Z}}}
1. {{{R[f]=Z/6}}}
Draining rate:{{{9*R[d]=Z}}}
2. {{{R[d]=Z/9}}}
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Filling while the drain is open for 6 hrs: {{{(R[f]-R[d])*6=Z1}}}
Find {{{Z1}}}.
Substituting from eq. 1 and eq. 2,
{{{(Z/6-Z/9)*6=Z1}}}
{{{Z1=Z(1-2/3)=Z/3}}}
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{{{Z-Z/3=(2/3)Z}}} still needs to be added
Find that time, now the drain has been closed.
{{{R[f]*t=(2/3)Z}}}
{{{(Z/6)*t=(2/3)Z}}}
{{{ t=4 }}} hrs
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Total time:{{{T=6+4}}}
{{{highlight(T=10 hrs)}}}