It takes an HP laserjet 1300 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 itself. Together the two printers can compl

a) Let's denote the time it takes the HP laserjet 1300 to complete the job alone as x. According to the problem, the HP laserjet 2420 completes the same job alone in 10 minutes less than the HP laserjet 1300, which means it takes x-10 minutes. We are also given that when working together, the two printers complete the job in 12 minutes. So we can set up the following equation: 1/x + 1/(x-10) = 1/12 We can solve for x using algebraic manipulation: 12(x-10) + 12x = x(x-10) 24x -120 = x^2 - 10x x^2 - 34x + 120 = 0 (x-30)(x-4) = 0 Therefore, x = 30 or x = 4. But x cannot equal 4 because it takes longer than 12 minutes for the HP laserjet 2420 to complete the job alone. Thus, x = 30 minutes is the solution. So it takes the HP laserjet 1300 printer 30 minutes to complete the 600-page print job alone, and it takes the HP laserjet 2420 printer 20 minutes to complete the same job alone. b) To find the speed in pages per minute of each printer, we simply divide 600 by the time it takes to complete the job alone. For the HP laserjet 1300: Speed = 600/30 = 20 pages per minute For the HP laserjet 2420: Speed = 600/20 = 30 pages per minute