Question 830661
Rates are best used in form and units of jobs per time.


ThreeTogether, 1/6 jobs per hour
manOne, ? 
manTwo, ?
manThree, {{{1/h}}}, where h is the number of hours for him to do 1 job alone.
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Work from manThree to get rate expressions for the other two men.
manTwo, {{{1/(h+6)}}}
manOne, {{{1/(2(h+6))}}}
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The only variable, and unknown, is still h, the time for manThree to do this one job of painting the barn if he worked alone.


The sum of the men's individual rates is the rate for all three men working at the same time.
{{{manOne+manTwo+manThree=ThreeTogether}}}
{{{highlight(1/(2(h+6))+1/(h+6)+1/h=1/6)}}}
Solve for h in that highlighted equation.  That will be the answer.