SOLUTION: It takes an HP LaserJet 1300 laser printer 10 minutes longer to complete a 600-page print job by itself than it takes an HP LaserJet 2420 to complete the same job by itself. Togeth

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Question 1207750: It takes an HP LaserJet 1300 laser printer 10 minutes longer to complete a 600-page print job by itself than it takes an HP LaserJet 2420 to complete the same job by itself. Together the two printers can complete the job in 12 minutes. How long does it take each printer to complete the print job alone? What is the speed of each printer?

Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!

It takes an HP LaserJet 1300 laser printer 10 minutes longer to complete a 600-page print job by itself than it takes an HP LaserJet 2420 to complete the same job by itself. Together the two printers can complete the job in 12 minutes. How long does it take each printer to complete the print job alone? What is the speed of each printer?
Let HP LaserJet 2420 take x hours to do the job of printing 600 pages
rate of doing work = 1/x
HP LaserJet 1300 laser printer 10 minutes longer = x+10 hours
rate of doing work 1/(x+10)
two printers can complete the job in 12 minutes
rate of doing work together is 1/12
Setup
1/x + 1/(x+10)= 1/12
Take LCM
(x+x+10)/x(x+10)= 1/12
(2x+10)/x(x+10)= 1/12
cross multiply
x(x+10)= 12(2x+10)
x^2+10x = 24x +120
x^2-14x-120=0
x^2-20x+6x-120=0
x(x-20)+6(x-20)=0
(x-20)(x+6)=0
x= 20 taking positive value
the slower printer takes 30 minutes and the faster 20 minutes

Answer by ikleyn(52817) (Show Source):
You can put this solution on YOUR website!
.

The solution by @mananth is correct, but I want to make one necessary correction.

The expression x*(x+10) is not an LCM (Least Common Multiple).

In this context, the correct mathematical name for this expression is " the common denominator ".