<PRE><B>Question 815652</B>
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/t}}} + {{{5/((t-2))}}} = 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)
{{{5/11.1}}} + {{{5/9.1}}} = 
.45 + .55 = 1.0</PRE>