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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 for each printer to complete the print job alone? What is the speed of each printer?
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Let x be the required time for the fast printer, in minutes.
Then the time for the slow printer is (x+12) minutes.
The rate of work of the fast printer, of the job per minute,
plus rate of work of the slow printer, of the job per minute,
is of the job per minute.
So, we write this rate of work equation
+ = . (1)
To solve it, we multiply all the terms by 12x*(x+10). It gives
12(x+10) + 12x = x*(x+10).
Simplify
12x + 120 + 12x = x^2 + 10x,
24x + 120 = x^2 + 10x
x^2 - 14x + 120 = 0.
Factor left sides
(x-20)*(x+6) = 0.
The roots are x= 20 and x= -6. We want the positive root (the time).
So, we take x = 20.
ANSWER. Fast printer will complete the job in 20 minutes working alone.
Slow printer will complete the job in 20+10 30 minutes working alone.
CHECK. I will check the validity of equation (1).
+ = + = = = .
Precisely correct !
Solved.