Word problem: A new photocopier can make 72 copies in 2 min. When the older photocopier is operational, the two photocopiers together can make 72 copies in 1.5 min. How long would it take the older photocopier to make 72 copies working alone? Show work.

Answer 1

rate of new = 72/2 copies/min
rate of old = 72/x copies/min

combined rate = 72/2 + 72/x
= (72x + 144)/(2x) copies per min

72/(72x+144)/(2x)) = 1.5
72(2x)/(72x+144) = 1.5
144x = 108x + 216
36x = 216
x = 6

rate of old machine = 72/6 or 12 copies/minute

Answer 2

Thanks much, that helps a lot.

Answer 3

or, consider this as the usual work problem, where the job is to make 72 copies.

1/1.5 = 1/x + 1/2 = 1/1.5
1/x = 2/3 - 1/2
1/x = 1/6
x = 6

It would have been a little more interesting if the number of copies given for each machine had been different. You might play around with that if you're curious.

Answer 4

Melissa Stone was just hired as a nurse at a hospital where she will earn $45,000 per year. If she receives a 6% raise each year, how much total money will she earn over the next 10 years?

Answer 5

$477000