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Working simultaneously at an identical constant rate, it takes 6 machi

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Working simultaneously at an identical constant rate, it takes 6 machi  [#permalink]

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New post 29 Aug 2017, 23:41
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Working simultaneously at an identical constant rate, it takes 6 machines 8 hours to produce y widgets. How many machines, working at that identical constant rate, are necessary to produce 2y widgets in 4 hours?

A. 6
B. 12
C. 18
D. 24
E. 48

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Working simultaneously at an identical constant rate, it takes 6 machi  [#permalink]

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New post 30 Aug 2017, 00:28
Bunuel wrote:
Working simultaneously at an identical constant rate, it takes 6 machines 8 hours to produce y widgets. How many machines, working at that identical constant rate, are necessary to produce 2y widgets in 4 hours?

A. 6
B. 12
C. 18
D. 24
E. 48


6 Machines -----8 Hours-----y widgets
So
6 Machines------4 Hours-----\(\frac{y}{2}\)widgets

But we need to produce 2y widgets in 4 hours.

To produce \(\frac{y}{2}\) widgets, we need 6 machines

So to produce 4*\(\frac{y}{2}\)widgets =2y widgets, we need 4*6 machines = 24 machines.

(D)
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Re: Working simultaneously at an identical constant rate, it takes 6 machi  [#permalink]

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New post 30 Aug 2017, 00:31
Bunuel wrote:
Working simultaneously at an identical constant rate, it takes 6 machines 8 hours to produce y widgets. How many machines, working at that identical constant rate, are necessary to produce 2y widgets in 4 hours?

A. 6
B. 12
C. 18
D. 24
E. 48


6 machines working for 8 hrs produce y widgets
? machines working for 4 hrs to produce 2y widgets

Multiplication factor for time is New/Old = 4/8
Multiplication factor for widgets is New/Old = 2y/y

No of machines is directly proportional to Number of widgets needed to be made and inversely proportional to the time allotted for the work.

Hence Number of new machines will be 6*(8/4)*(2y/y) = 24

Hence answer should be D. 24

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Re: Working simultaneously at an identical constant rate, it takes 6 machi  [#permalink]

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New post 30 Aug 2017, 00:32
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Bunuel wrote:
Working simultaneously at an identical constant rate, it takes 6 machines 8 hours to produce y widgets. How many machines, working at that identical constant rate, are necessary to produce 2y widgets in 4 hours?

A. 6
B. 12
C. 18
D. 24
E. 48


6 m + 8 h = Y w
12 m + 8 h = 2Y w
24 m + 4 h = 2Y w

D
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Working simultaneously at an identical constant rate, it takes 6 machi  [#permalink]

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New post 30 Aug 2017, 16:49
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Bunuel wrote:
Working simultaneously at an identical constant rate, it takes 6 machines 8 hours to produce y widgets. How many machines, working at that identical constant rate, are necessary to produce 2y widgets in 4 hours?

A. 6
B. 12
C. 18
D. 24
E. 48

# of machines(M) * rate * time = Work

The individual machine rate for 6 machines to produce y widgets in 8 hours is

\(\frac{y}{(6*8)}\) = \(\frac{y}{48}\)

To produce 2y widgets in 4 hours, working at that rate, it will take how many machines, M?

M * \(\frac{y}{48} * 4 = 2y\)

M = \(\frac{2y}{(\frac{4y}{48})}\), or

M = \(2y *
\frac{48}{4y}\) = 24 machines

Answer D
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Re: Working simultaneously at an identical constant rate, it takes 6 machi  [#permalink]

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New post 02 Sep 2017, 07:17
1
Bunuel wrote:
Working simultaneously at an identical constant rate, it takes 6 machines 8 hours to produce y widgets. How many machines, working at that identical constant rate, are necessary to produce 2y widgets in 4 hours?

A. 6
B. 12
C. 18
D. 24
E. 48


We are given that the rate of 6 machines is y/8. Using a proportion, we can determine how many machines work at a rate of 2y/4 = y/2.

6/(y/8) = n/(y/2)

48/y = 2n/y

48y = 2ny

24 = n

Alternate solution:

We see that the number of widgets needed to be produced (2y) is twice the given number of widgets (y). Thus, we need to double 6 machines to 12 machines so that in 8 hours they can produce 2y widgets. However, we see we need to produce these 2y widgets in 4 hours, which is half of the given 8 hours. Thus, we need to double the machines again from 12 machines to 24 machines to produce 2y widgets in 4 hours.

Answer: D
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Working simultaneously at an identical constant rate, it takes 6 machi  [#permalink]

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New post 06 Sep 2017, 00:39
Bunuel wrote:
Working simultaneously at an identical constant rate, it takes 6 machines 8 hours to produce y widgets. How many machines, working at that identical constant rate, are necessary to produce 2y widgets in 4 hours?

A. 6
B. 12
C. 18
D. 24
E. 48


Let y = 24
Rates * Time = Work
(1/2*6) * 8 = 24=> (1/2*6) * 4 =12=> (1/2*x) *4 =48

1/2X * 4 =48
=>X = 24

Answer D
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Re: Working simultaneously at an identical constant rate, it takes 6 machi  [#permalink]

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New post 06 Sep 2017, 04:01
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2
Bunuel wrote:
Working simultaneously at an identical constant rate, it takes 6 machines 8 hours to produce y widgets. How many machines, working at that identical constant rate, are necessary to produce 2y widgets in 4 hours?

A. 6
B. 12
C. 18
D. 24
E. 48


To produce y widget 6*8 = 48 Machine - hours are required
To produce 2y widget 48*2 = 96 Machine - hours are required
To produce 2y widget in 4 hours, 96/4 = 24 Machines are required. .... Answer D
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Re: Working simultaneously at an identical constant rate, it takes 6 machi  [#permalink]

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New post 06 Sep 2017, 08:19
JeffTargetTestPrep wrote:
Bunuel wrote:
Working simultaneously at an identical constant rate, it takes 6 machines 8 hours to produce y widgets. How many machines, working at that identical constant rate, are necessary to produce 2y widgets in 4 hours?

A. 6
B. 12
C. 18
D. 24
E. 48


We are given that the rate of 6 machines is y/8. Using a proportion, we can determine how many machines work at a rate of 2y/4 = y/2.

6/(y/8) = n/(y/2)

48/y = 2n/y

48y = 2ny

24 = n

Alternate solution:

We see that the number of widgets needed to be produced (2y) is twice the given number of widgets (y). Thus, we need to double 6 machines to 12 machines so that in 8 hours they can produce 2y widgets. However, we see we need to produce these 2y widgets in 4 hours, which is half of the given 8 hours. Thus, we need to double the machines again from 12 machines to 24 machines to produce 2y widgets in 4 hours.

Answer: D


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Re: Working simultaneously at an identical constant rate, it takes 6 machi  [#permalink]

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New post 06 Sep 2017, 21:20
1
[quote="Bunuel"]Working simultaneously at an identical constant rate, it takes 6 machines 8 hours to produce y widgets. How many machines, working at that identical constant rate, are necessary to produce 2y widgets in 4 hours?

A. 6
B. 12
C. 18
D. 24
E. 48[/quote

6*R*8= y;
Given same rate so N*R*4=2y;
N*R*4= 2*6*R*8
N=96/4= 24

Ans:D
Re: Working simultaneously at an identical constant rate, it takes 6 machi &nbs [#permalink] 06 Sep 2017, 21:20
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