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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42 GPA: 3.82
There are 3 machines with the same work rate. If it took t hours for 3  [#permalink]

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Difficulty:   15% (low)

Question Stats: 79% (01:43) correct 21% (01:47) wrong based on 143 sessions

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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 t?

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

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Math Expert V
Joined: 02 Aug 2009
Posts: 7960
Re: There are 3 machines with the same work rate. If it took t hours for 3  [#permalink]

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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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Location: India
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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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2
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

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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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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
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42 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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=>

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.

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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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1
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

Dear Moderator,
There seems to be a small typo here. Variable K has been mistakenly written instead of variable t. Hope you will look into this. Thank you.
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- Stne
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: There are 3 machines with the same work rate. If it took t hours for 3  [#permalink]

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stne wrote:
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

Dear Moderator,
There seems to be a small typo here. Variable K has been mistakenly written instead of variable t. Hope you will look into this. Thank you.

_______________
Edited. Thank you.
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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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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 t?

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

Let efficiency of each machine be "e"

So, $$3*e*t = 2*e*(t+2)$$

Or, $$3t = 2t + 4$$

Or, $$t = 4$$, Answer must be (A) 4
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Joined: 16 May 2017
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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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t/t+2=2/3
So, 3t=2t+4
=> t=4 hrs.
(A) Re: There are 3 machines with the same work rate. If it took t hours for 3   [#permalink] 01 Oct 2018, 06:46
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