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There are 4 machines with the same work rate. If it took k hours for 3

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Math Revolution GMAT Instructor
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There are 4 machines with the same work rate. If it took k hours for 3  [#permalink]

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New post 01 Mar 2018, 03:50
1
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A
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E

Difficulty:

  35% (medium)

Question Stats:

70% (01:51) correct 30% (01:52) wrong based on 100 sessions

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[GMAT math practice question]

There are 4 machines with the same work rate. If it took \(k\) hours for 3 machines to work and did \(k-2\) hours for 4 machines when working together, what is the value of \(k\)?

A. 4
B. 5
C. 6
D. 7
E. 8
Spoiler: OA

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Re: There are 4 machines with the same work rate. If it took k hours for 3  [#permalink]

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New post 01 Mar 2018, 05:33
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2
If it takes 3 machines khours to work and 4 machine (k-2)hrs, then
1 machine will work in 3k hours which is also equivalent to 4(k-2) hours
Therefore
3k=4k-8
K=8

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Math Revolution GMAT Instructor
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Re: There are 4 machines with the same work rate. If it took k hours for 3  [#permalink]

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New post 04 Mar 2018, 19:25
=>

Work Amount = Number of machines * Work Rate * Time
If r is the machine’s work rate, we have \(3rk = 4r(k-2)\) or \(3k = 4k -8\).
Thus \(k = 8\).

Therefore, E is the answer.

Answer: E
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Re: There are 4 machines with the same work rate. If it took k hours for 3  [#permalink]

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New post 10 Jun 2019, 19:24
1
MathRevolution wrote:
[GMAT math practice question]

There are 4 machines with the same work rate. If it took \(k\) hours for 3 machines to work and did \(k-2\) hours for 4 machines when working together, what is the value of \(k\)?

A. 4
B. 5
C. 6
D. 7
E. 8

Let the rate of each machine be r. We can create the equation:

(3r)k = (4r)(k - 2)

3k = 4k - 8

8 = k

Answer: E
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Re: There are 4 machines with the same work rate. If it took k hours for 3   [#permalink] 10 Jun 2019, 19:24
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