SOLUTION: It takes Denis 3 hrs longer than Rolly to complete a certain job. Working together, both can complete the job in 2 hrs. How long does it take each person to complete the job workin

Question 652519: It takes Denis 3 hrs longer than Rolly to complete a certain job. Working together, both can complete the job in 2 hrs. How long does it take each person to complete the job working alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
It takes Denis 3 hrs longer than Rolly to complete a certain job.
Working together, both can complete the job in 2 hrs.
How long does it take each person to complete the job working alone?
:
let r = time required by Rolly alone
then
(r+3) = time required by Denis
:
Let the completed job = 1
:
A shared work equation
:
+ = 1
multiply by r(r+3), results
2(r+3) + 2r = r(r+3)
:
2r + 6 + 2r = r^2 + 3r
Combine like terms on the right
0 = r^2 + 3r - 2r - 2r - 6
A quadratic equation
r^2 - r - 6 = 0
Factors to
(r-3)(r+2) = 0
the positive solution
r = 3 hrs, Rolly working alone
then
3 + = 6 hrs, Denis working alone
:
:
Check this
2/3 + 2/6 = 1
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