SOLUTION: an office has an old copying machine and a new one. Working together, it takes both machines 8 hours to make all the copies of the annual financial report. Working alone, it takes

Question 526636: an office has an old copying machine and a new one. Working together, it takes both machines 8 hours to make all the copies of the annual financial report. Working alone, it takes the old copying machine 30 hours longer than the new one to make all the copies of the report. How long would it take the new copying machine to make all the copies working alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
an office has an old copying machine and a new one.
Working together, it takes both machines 8 hours to make all the copies of the annual financial report.
Working alone, it takes the old copying machine 30 hours longer than the new one to make all the copies of the report.
How long would it take the new copying machine to make all the copies working alone?
:
let t = new copy machine time alone
then
(t+30) = old machine alone
:
Let the completed job = 1
:
A typical shared work equation
+ = 1
multiply by t(t+30), results
8(t+30) + 8t = t(t+30)
8t + 240 + 8t = t^2 + 30t
16t + 240 = t^2 + 30t
0 = t^2 + 30t - 16t - 240
A quadratic equation
t^2 + 14t - 240 = 0
You can use the quadratic formula here, but this will factor to:
(t+24)(t-10) = 0
the positive solution
t = 10 hrs required by the new machine to complete the job
:
:
Check this
8/10 + 8/40 =
.8 + .2 = 1
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