Question 354828
Rate*Time=Output
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Let {{{P}}} be the output required to fill the pool.
Find each person's rate. 
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Jim:{{{R[j]*30=P}}}
{{{R[j]=P/30}}}
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Sue:{{{R[s]*45=P}}}
{{{R[s]=P/45}}}
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Tony:{{{R[t]*90=P}}}
{{{R[t]=P/90}}}
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Their output all together, 
{{{(R[j]+R[s]+R[t])*t=P}}}
Substituting,
{{{(P/30+P/45+P/90)*t=P}}}
{{{(3/90+2/45+1/90)*t=1}}}
{{{(6/90)*t=1}}}
{{{highlight(t=15)}}} minutes.