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?
Answers
Reiny
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
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
Damon
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
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