Working alone at its constant rate, machine $K$ took 3 hours to produce 1/4 of the units produced last Friday. Then

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Sun May 31, 2020 12:45 pm

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Working alone at its constant rate, machine $K$ took 3 hours to produce 1/4 of the units produced last Friday. Then machine $M$ started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine $M,$ working alone at its constant rate, to produce all of the units produced last Friday?

A. 8
B. 12
C. 16
D. 24
E. 30

[spoiler]OA=D[/spoiler]

Source: Official Guide

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Source: Beat The GMAT — Problem Solving | Sun May 31, 2020 12:45 pm

JamesHammel: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Sun May 31, 2020 4:19 pm

Re: Working alone at its constant rate, machine $K$ took 3 hours to produce 1/4 of the units produced last Friday. The

by JamesHammel » Sun May 31, 2020 5:43 pm

3/4 of the production is left.
Together, both machines take 6 hours to complete 3/4 of the product

In those 6 hours, K can produce 2/4 of the product (1/4 * 2).
This means M produced 1/4 in 6 hours.

It would take M 6*4 hours to complete production alone. (D)

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8208; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: Working alone at its constant rate, machine $K$ took 3 hours to produce 1/4 of the units produced last Friday. The

by Scott@TargetTestPrep » Wed Mar 31, 2021 8:42 am

M7MBA wrote: ↑
Sun May 31, 2020 12:45 pm
Working alone at its constant rate, machine $K$ took 3 hours to produce 1/4 of the units produced last Friday. Then machine $M$ started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine $M,$ working alone at its constant rate, to produce all of the units produced last Friday?

A. 8
B. 12
C. 16
D. 24
E. 30

[spoiler]OA=D[/spoiler]

Source: Official Guide

Solution:

Since it takes machine K 3 hours to produce 1/4 of the units, machine K’s rate is (1/4)/3 = 1/12. If we let m be the number of hours it takes machine M to produce all the units by itself, then machine M’s rate is 1/m. Since it takes both machines 6 hours to produce the rest of the units (i.e., 3/4 of the units), we can create the equation:

(1/12 + 1/m) x 6 = 3/4

1/12 + 1/m = 1/8

1/m = 1/24

m = 24

Answer: D

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