Machine X produces cartons at a uniform rate of 90 every 3

[BTGModeratorVI]

Machine X produces cartons at a uniform rate of 90 every 3 minutes, and Machine Y produces cartons at a uniform rate of 100 every 2 minutes. Working simultaneously, the two machines would produce a total of 560 cartons in how many minutes?

(A) 7
(B) 6
(C) 5
(D) 4
(E) 3

Answer: A
Source: Manhattan prep

[Scott@TargetTestPrep]

Machine X produces cartons at a uniform rate of 90 every 3 minutes, and Machine Y produces cartons at a uniform rate of 100 every 2 minutes. Working simultaneously, the two machines would produce a total of 560 cartons in how many minutes?

(A) 7
(B) 6
(C) 5
(D) 4
(E) 3

Answer: A

Solution:

We see that Machine X’s rate is 90/3 = 30 cartons per minute and Machine Y’s rate is 100/2 = 50 cartons per minute. Therefore, their combined rate is 30 + 50 = 80 cartons per minute and it will take 560/80 = 7 minutes to produce a total 560 cartons when the two machines work simultaneously.

Answer: A