Question 359395
Rate*Time=Output
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Let the tank volume be {{{V}}}.
Find the fill rate,
{{{R[f]*t=V}}}
{{{R[f]*4=V}}}
{{{R[f]=V/4}}}
Find the drain rate,
{{{R[d]*t=V}}}
{{{R[d]*6=V}}}
{{{R[d]=V/6}}}
Now find the time to fill the tank when both valves are open,
{{{(R[f]-R[d])*t=V}}}
{{{(V/4-V/6)*t=V}}}
{{{(1/4-1/6)*t=1}}}
{{{(3/12-2/12)*t=1}}}
{{{(1/12)*t=1}}}
{{{highlight(t=12)}}}hours