SOLUTION: It takes Tom 3 hours less to paint a fence than it does Jim. If the two boys work together, they can paint the fence in 2 hours. How many hours would each boym working alone need t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes Tom 3 hours less to paint a fence than it does Jim. If the two boys work together, they can paint the fence in 2 hours. How many hours would each boym working alone need t      Log On


   



Question 128209: It takes Tom 3 hours less to paint a fence than it does Jim. If the two boys work together, they can paint the fence in 2 hours. How many hours would each boym working alone need to paint the fence?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of doing work
(1 fence) / (Tom's time to paint it) + (1 fence) / (Jim's time to paint it) =
(1 fence) / (the time it takes them working together)
Let j = Jim's time to paint the fence
1+%2F+%28j+-+3%29+%2B+1+%2F+j+=+1+%2F+2
multiply both sides by 2%2Aj%2A%28j+-+3%29
2j+%2B+2%28j+-+3%29+=+j%2A%28j+-+3%29
2j+%2B+2j+-+6+=+j%5E2+-+3j
j%5E2+-+7j+%2B+6+=+0
%28j+-+6%29%28j+-+1%29+=+0
The solutions are j+=+6 and j+=+1
I'm going to reject j+=+1 as a solution,
since Tom's time which is j+-+3 would
be negative.
Jim's time working alone is 6 hours
and Tom's time working alone is 3 hours
check:
1%2F3+%2B+1%2F6+=+1%2F2
2%2F6+%2B+1%2F6+=+1%2F2
3%2F6+=+1%2F2
1%2F2+=+1%2F2
OK