SOLUTION: it takes two laser printers 12 minutes, working together, to complete a 680 page print job. If each printer is printing each job alone, the first laser printer takes 10 minutes lon

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Question 629359: it takes two laser printers 12 minutes, working together, to complete a 680 page print job. If each printer is printing each job alone, the first laser printer takes 10 minutes longer than the second laser printer. How long does it take each printer to complete the printing job alone? What is the speed of each printer?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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it takes two laser printers 12 minutes, working together, to complete a
680 page print job.
If each printer is printing each job alone, the first laser printer takes 10
minutes longer than the second laser printer.
How long does it take each printer to complete the printing job alone?
:
Let t = time required 2nd printer working alone
then
(t+10) = time required by the 1st printer alone
:
Let the completed job = 1 (printing of 680 pages)
:
A shared work equation
12%2Ft + 12%2F%28%28t%2B10%29%29 = 1
multiply by t(t+10) to clear the denominators, results:
12(t+10) + 12t = t(t+10)
12t + 120 + 12t = t^2 + 10t
Arrange as a quadratic equation on right
0 = t^2 + 10t - 24t - 120
t^2 - 14t - 120 = 0
Factors
(t-20)(t+6) = 0
the positive solution
t = 20 minutes time of the 2nd printer
then
20 + 10 = 30 min time of the 1st printer
:
"What is the speed of each printer?"
1st printer: 680/30 = 222%2F3 pages/min
2nd printer: 680/20 = 34 pages/min