SOLUTION: Jose and Carl together can retile a roof in 10 hours. Working alone, Jose could do the job 4.5 hours faster than Carl. How long would each man need to work to do the job himself?

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Question 691561: Jose and Carl together can retile a roof in 10 hours. Working alone, Jose could do the job 4.5 hours faster than Carl. How long would each man need to work to do the job himself?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jose and Carl together can retile a roof in 10 hours.
Working alone, Jose could do the job 4.5 hours faster than Carl.
How long would each man need to work to do the job himself?
:
Let j = Jose's time to do the job
then
(j+4.5) = Carl's time
:
Let the competed job = 1
:
10%2Fj + 10%2F%28%28j%2B4.5%29%29 = 1
multiply by j(j+4.5) to clear the denominators, results:
10(j+4.5) + 10j = j(j+4.5)
10j + 45 + 10j = j^2 + 4.5j
A quadratic equation
0 = j^2 + 4.5j - 20j -45
j^2 - 15.5j - 45 = 0
:
solve this, the positive solution; j = 18 hrs