jenny's company has two photocopying machines, one of which is older and slower than the other. In fact, the newer machine can put out four-thirds as many copies as the older machine in the same amount of time. If, while running at the same time, together they produce 560 copies, how many copies did each machine produce?

Question

jenny's company has two photocopying machines, one of which is older and slower than the other. In fact, the newer machine can put out four-thirds as many copies as the older machine in the same amount of time. If, while running at the same time,  together they produce 560 copies, how many copies did each machine produce?

Reiny · Answer

rate of older machine === 1 unit/unit of time
rate of newer machine === 4/3 units/unit of time

combined rate = 1 + 4/3 = 7/3 units/unit of time

(7/3)x = 560
x = 240

The slower did 240 copies
and the faster did (4/3)(240) or 320 copies