SOLUTION: Please help solve this problem....thanks. George can cut and split a cord of firewood in 3 fewer hour(s) than Skylar can. When they work togethe it takes them 2 hr(s).How long w

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Please help solve this problem....thanks. George can cut and split a cord of firewood in 3 fewer hour(s) than Skylar can. When they work togethe it takes them 2 hr(s).How long w      Log On


   

Question 582010: Please help solve this problem....thanks.
George can cut and split a cord of firewood in 3 fewer hour(s) than Skylar can. When they work togethe it takes them 2 hr(s).How long would it take each of them to do the job alone?
George?
Skylar?
Simplify answer
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes Skyler to do the job
Then (x-3) = amount of time it takes George to do the job
Skyler works at the rate of 1/x job per hour
George works at the rate of 1/(x-3) job per hour
Together they work at the rate of 1/2 of the job per hour
sooooo:
1/x +1/(x-3)=1/2 multiply each side by 2x(x-3)
2(x-3)+2x=x(x-3) simplify
2x-6+2x=x^2-3x collect like terms
4x-6=x^2-3x
x^2-7x+6=0 quadratic in standard form and it can be factored
(x-6)(x-1)=0
x=6
and
x=1 Clearly x=1 does not work because George would have do do negative work to do the job in 3 hours fewer time, sooooo
x=6 hours time time it takes Skyler to do the job
x-3=6-3=3 hours time it takes George to do the job
CK
1/6+1/3=1/2
1/6 + 2/6=1/2
1/2=1/2
Hope this helps---ptaylor