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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

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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

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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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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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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