Question 770574
Let h = the time in hours for Allen to do the job by himself.


PERSONS_______________RATE jobs per hour
Sean&Allen____________{{{1/9}}}
Allen_________________{{{1/h}}}
Sean__________________{{{1/((1/3)h)}}}


Sean's rate when simplified is 3/h jobs per hour.


When the persons work at the same time on the same job, their rates are simple additions, or simple sum.

Allen rate + Sean Rate = Allen& Sean Together rate
{{{highlight(1/h+3/h=1/9)}}}
Solve for h.


The best way to start from the equation is multiply left and right sides by the lowest common denominator of 9h which will clear the fractions.
{{{9h(1/h)+9h(3/h)=9h(1/9)}}}
and you simplify and solve from there...