SOLUTION: Joe can cut and split a cord of firewood in 9 fewer hr(s) than Suzie can. When they work together, it takes them 6 hour(s). How long would it take each of themm to do the same job

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Joe can cut and split a cord of firewood in 9 fewer hr(s) than Suzie can. When they work together, it takes them 6 hour(s). How long would it take each of themm to do the same job      Log On


   

Question 864286: Joe can cut and split a cord of firewood in 9 fewer hr(s) than Suzie can. When they work together, it takes them 6 hour(s). How long would it take each of themm to do the same job alone?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Joe can cut and split a cord of firewood in 9 fewer hr(s) than Suzie can. When they work together, it takes them 6 hour(s). How long would it take each of them to do the same job alone?
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let x=hours Suzie can finish the job alone
1/x=her work rate
x-9=hours Joe can finish the job alone
1/(x-9)=his work rate
1/6=work rate of Joe and Suzie working together
...
sum of individual work rates equal work rate working together
1%2Fx%2B1%2F%28x-9%29=1%2F6
LCD:6x(x-9)
6(x-9)+6x=x(x-9)
6x-54+6x=x^2-9x
x^2-21x+54=0
(x-18)(x-3)=0
x=3(reject, not reasonable)
or
x=18
x-9=9
hours Suzie can finish the job alone=18
hours Joe can finish the job alone=9