Printing machine A and printing machine B print the same newspaper printout, but machine B prints at half the rate of machine A. If each machine produces 200 newspaper printouts, and both operate at different times for a total of 4 hours, what is the rate of each printing machine

Let us assume the rate of printing in machine A is x per hour and the rate for machine B is y. Given that machine B prints at half the rate of machine A, therefore:

y = (1/2)x (1)

Also, both machine produces 200 newspaper printouts, and both operate at different times for a total of 4 hours. Therefore:

200/x + 200/y = 4 (2)

Put y = (1/2)x in equation:

[tex]\frac{200}{x}+\frac{200}{(\frac{1}{2} )x}=4\\ \\ \frac{200}{x}+\frac{400}{x}=4\\\\Multiply\ through\ by\ x:\\\\200+400=4x\\\\4x=600\\\\x=150[/tex]

Put x = 150 in equation y:

y=(1/2)150 = 75

Therefore the rate of machine A is 150 newspapers per hour while that of machine B is 75 newspapers per hour