SOLUTION: A and B working together can complete a job in 7 1/2 hours. Working alone, A takes 8 hours longer than B to do the job. How long would it take each working alone?

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Question 698103: A and B working together can complete a job in 7 1/2 hours. Working alone, A takes 8 hours longer than B to do the job. How long would it take each working alone?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A and B working together can complete a job in 7 1/2 hours.
Working alone, A takes 8 hours longer than B to do the job.
How long would it take each working alone
:
Let b = B's time working alone
A takes 8 hrs longer, therefore
(b+8) = A's time alone
Let the completed job = 1
:
7.5%2Fb + 7.5%2F%28%28b%2B8%29%29 = 1
multiply by b(b+8), resulting in:
7.5(b+8) + 7.5b = b(b+8)
7.5b + 60 + 7.5b = b^2 + 8b
A quadratic equation
0 = b^2 + 8b - 15b - 60
b^2 - 7b - 60 = 0
Factors to
(b-12)(b+5) = 0
the positive solution
b = 12 hours, B working alone
then
12 + 8 = 20 hrs A working alone
:"
:
See it that checks out
7.5/12 + 7.5/20 =
.625 + .375 = 1; confirms our solutions