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# There are 3 machines with the same work rate. If it took t hours for 3

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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There are 3 machines with the same work rate. If it took t hours for 3 [#permalink]

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24 Oct 2017, 06:54
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[GMAT math practice question]

There are 3 machines with the same work rate. If it took t hours for 3 machines to work and took t+2 hours for 2 machines when working together, what is the value of k?

A. 4
B. 5
C. 6
D. 7
E. 9
[Reveal] Spoiler: OA

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

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24 Oct 2017, 07:08
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MathRevolution wrote:
[GMAT math practice question]

There are 3 machines with the same work rate. If it took t hours for 3 machines to work and took t+2 hours for 2 machines when working together, what is the value of k?

A. 4
B. 5
C. 6
D. 7
E. 9

I am sure Q is asking value of t and k is a typo error..

speed si the same..
if 3 do it in t hours, ONE will do it in 3*t..
if 2 do it in t+2 hours, ONE will do it in 2*(t+2)=2t+4..

But the speed is SAME, so 3t=2t+4....t=4
A
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Re: There are 3 machines with the same work rate. If it took t hours for 3 [#permalink]

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24 Oct 2017, 07:38
The rate of work of each machine is the same.
Work done by 3 machines in 1 hr = $$\frac{1}{t}$$
Work done by 1 machine in 1 hr = $$\frac{1}{{3t}}$$
Work done by 2 machines in 1 hr = $$\frac{2}{{3t}}$$ = $$\frac{1}{{t+2}}$$
$$\frac{2}{{3t}}$$=$$\frac{1}{{t+2}}$$
2t+4=3t
t=4

Answer A

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There are 3 machines with the same work rate. If it took t hours for 3 [#permalink]

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24 Oct 2017, 12:31
There are 3 machines with the same work rate. If it took t hours for 3 machines to work and took t+2 hours for 2 machines when working together, what is the value of k?

A. 4
B. 5
C. 6
D. 7
E. 9

2/3 rate➡3/2 time
3/2*t=t+2
t=4 hours
A
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Posts: 4920
GPA: 3.82
Re: There are 3 machines with the same work rate. If it took t hours for 3 [#permalink]

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25 Oct 2017, 23:46
=>

Assume X is the time one machine takes to work.

1/T=3/X and 1/T+2=2/X

X = 3T and X = 2(T+2).
We have 3T = 2T + 4 or T = 4.

Thus, the answer is A.

Answer: A
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Re: There are 3 machines with the same work rate. If it took t hours for 3   [#permalink] 25 Oct 2017, 23:46
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# There are 3 machines with the same work rate. If it took t hours for 3

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