SOLUTION: When Sean and Allen work together, they can paint a fence in 9 hours. Working alone,Sean can paint the fence in 1/3 of the amount of time that it takes Allen to paint the fence. H

Algebra ->  Rate-of-work-word-problems -> SOLUTION: When Sean and Allen work together, they can paint a fence in 9 hours. Working alone,Sean can paint the fence in 1/3 of the amount of time that it takes Allen to paint the fence. H      Log On


   

Question 770574: When Sean and Allen work together, they can paint a fence in 9 hours. Working alone,Sean can paint the fence in 1/3 of the amount of time that it takes Allen to paint the fence. How long would it take Allen to paint the fence alone?
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Let h = the time in hours for Allen to do the job by himself.

PERSONS_______________RATE jobs per hour
Sean&Allen____________1%2F9
Allen_________________1%2Fh
Sean__________________1%2F%28%281%2F3%29h%29

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%281%2Fh%2B3%2Fh=1%2F9%29
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%281%2Fh%29%2B9h%283%2Fh%29=9h%281%2F9%29
and you simplify and solve from there...