SOLUTION: I'm completely stumped on this word problem, and it would mean so much for some help. it takes an hp laserjet 1300 10 minutes longer to complete a 600-page print job by itself

Question 793474: I'm completely stumped on this word problem, and it would mean so much for some help.
it takes an hp laserjet 1300 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 job alone? what is the speed of each printer?
Thank you very much<3
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
it takes an hp laserjet 1300 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 job alone? what is the speed of each printer?
============
HP 2420 DATA:
time = x min/job ; rate = (1/x) job/min
------------------------
HP 1300 DATA:
time = (x+10) min/job ; rate = 1/(x+10) = job/min
--------
Together DATA:
time = 12 min/job ; rate = 1/12 job/min
------------------------------------------
Equation:
rate + rate = together rate
1/x + 1/(x+10) = 1/12
-----------------------------
12(x+10) + 12x = x(x+10)
---------
12x + 120 + 12x = x^2 + 10x
------
x^2 + -14x - 120 = 0
------
x = 20 min (HP 2420 time to do the job)
x + 10 = 30 min (HP 1300 time to do the job)
==================
Cheers,
Stan H.
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