Question

One copy machine can run off copies in 170 minutes. A newer machine can do the same job in 119 minutes. How long does it take the two​ machines, working​ together, to make all of the necessary​ copies?

Answer 1

rate of old machine = 1/170
rate of new machine = 1/119
combined rate = 1/170 + 1/119

time at combined rate = 1/(1/170+1/119)
= 1/(1/70) = 70 minutes

Answer 2

machine 1 does n copies/170 min
so n/170 copies/min

machine 2 does n/119 copies/min
so

n = (n/170 + n/119) t
1/t = 1/170+1/119 = .014286
so
t = 70 min