SOLUTION: office has an old copying machine and a new one. together it takes both machines 4 hours to copy all financial reports. alone it takes the old copier 15 hours longer than the new o

Algebra ->  Rate-of-work-word-problems -> SOLUTION: office has an old copying machine and a new one. together it takes both machines 4 hours to copy all financial reports. alone it takes the old copier 15 hours longer than the new o      Log On


   

Question 405292: office has an old copying machine and a new one. together it takes both machines 4 hours to copy all financial reports. alone it takes the old copier 15 hours longer than the new one to make all copies . how long will it take the new copying machine to make all the copies
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
office has an old copying machine and a new one.
together it takes both machines 4 hours to copy all financial reports.
alone it takes the old copier 15 hours longer than the new one to make all copies .
how long will it take the new copying machine to make all the copies
-------------------------
New copier DATA:
time = x hrs/job ; rate = 1/x job/hr
-----
Old copier DATA:
time = (x+15) hrs/job ; rate = 1/(x+15)job/hr
----
Together DATA:
time = 4 hrs/job ; rate = 1/4 job/hr
==========================================
Equation:
rate + rate = together rate
1/x + 1/(x+15) = 1/4
Multiply thru by 4x(x+15) to get:
4(x+15) + 4x = x(x+15)
---
4x + 60 + 4x = x^2+15x
---
x^2 + 7x - 60 = 0
x^2+12x-5x-60 = 0
x(x+12)-5(x+12) = 0
(x+12)(x-5) = 0
Positive solution:
x = 5 hrs (time for the new machine)
x+15 = 20 hrs (time for the old machine)
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Cheers,
Stan H.