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

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pm; Followed by:1 members

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

by BTGModeratorVI » Wed Jan 06, 2021 8:15 am

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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
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Source: Beat The GMAT — Problem Solving | Wed Jan 06, 2021 8:15 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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

by Scott@TargetTestPrep » Thu Jan 14, 2021 4:39 am

BTGModeratorVI wrote: ↑
Wed Jan 06, 2021 8:15 am
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

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