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

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 !