SOLUTION: Please help me with this word problem. Working together, two people can clean an office building in 5 hr. One person is new to the job and would take 2 hr longer than the other p

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Question 815652: Please help me with this word problem.
Working together, two people can clean an office building in 5 hr. One person is new to the job and would take 2 hr longer than the other person to clean the building alone. How long would it take the new worker to clean the building alone?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Working together, two people can clean an office building in 5 hr.
One person is new to the job and would take 2 hr longer than the other person to clean the building alone.
How long would it take the new worker to clean the building alone?
:
Let t = time required by the new guy to do the job
then
(t-2) = time required by the old guy
:
Let the completed job = 1 (a clean office building)
:
A shared work equation
5%2Ft + 5%2F%28%28t-2%29%29 = 1
multiply t(t-2) to clear the denominators, results:
5(t-2) + 5t = t(t-2)
5t - 10 + 5t = t^2 - 2t
10t - 10 = t^2 - 2t
Arrange as a quadratic on the right
0 = t^2 - 2t - 10t + 10 = 0
t^2 - 12t + 10 = 0
Use the quadratic formula to find t
I got a reasonable answer of 11.1 hrs for the new guy
:
:
Check this (Old guy takes 9.1 hrs alone)
5%2F11.1 + 5%2F9.1 =
.45 + .55 = 1.0