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Nine identical machines, each working at the same constant rate, can 03 Jul 2018, 00:04
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Nine identical machines, each working at the same constant rate, can stitch 27 jerseys in 4 minutes. How many minutes would it take 4 such machines to stitch 60 jerseys?

(A) 8
(B) 12
(C) 16
(D) 18
(E) 20
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E
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Nine identical machines, each working at the same constant rate, can 03 Jul 2018, 02:26
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9 machine stitches 27 jersey in 4 minutes
1 machines stitches 1 jersey in (4 * 9)/ 27 minutes. = 4/3
4 machines stitches 60 jersey in (4*60)/3*4 = 20 minutes
Option E
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Nine identical machines, each working at the same constant rate, can 03 Jul 2018, 03:31
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Bunuel
Nine identical machines, each working at the same constant rate, can stitch 27 jerseys in 4 minutes. How many minutes would it take 4 such machines to stitch 60 jerseys?

(A) 8
(B) 12
(C) 16
(D) 18
(E) 20

Using M1D1H1/W1=M2D2H2/W2
W1=27
W2=60

9*4/27=4*m*/60
9*60=m*27=20 minutes
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Nine identical machines, each working at the same constant rate, can 03 Jul 2018, 13:10
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Bunuel
Nine identical machines, each working at the same constant rate, can stitch 27 jerseys in 4 minutes. How many minutes would it take 4 such machines to stitch 60 jerseys?

(A) 8
(B) 12
(C) 16
(D) 18
(E) 20
If you like R*T=W, one method is to add (# of machines) to LHS

Scenario # 1: Find rate of one machine
\(9\) machines need \(4\) minutes to make \(27\) jerseys
Rate of one machine in \(\frac{jerseys}{minutes}\)?
(# of machines) * R * T = W
\((9) * R * (4) = 27\)
\(R* 36 = 27\)
\(R=\frac{27}{36}=\frac{3}{4}\)

At that rate, how many minutes do 4 such machines require to stitch 60 jerseys?

Scenario # 2 - Find time
4 machines must sew 60 jerseys at rate of \(\frac{3}{4}\)
Time needed?
(# of machines) * R * T = W
\((4)*(\frac{3}{4})*T=60\)
\(T*3=60\)
\(T=20\) minutes

Answer E
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Nine identical machines, each working at the same constant rate, can 23 Jan 2020, 10:07
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Bunuel
Nine identical machines, each working at the same constant rate, can stitch 27 jerseys in 4 minutes. How many minutes would it take 4 such machines to stitch 60 jerseys?

(A) 8
(B) 12
(C) 16
(D) 18
(E) 20

The rate of 9 machines is 27/4. To determine the rate of 4 machines, we can create the proportion:

9/(27/4) = 4/n

36/27 = 4/n

4/3 = 4/n

4n = 12

n = 3

So, it will take 4 machines 60/3 = 20 minutes to stitch 60 jerseys.

Answer: E
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Nine identical machines, each working at the same constant rate, can 25 May 2022, 10:31
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Bunuel
Nine identical machines, each working at the same constant rate, can stitch 27 jerseys in 4 minutes. How many minutes would it take 4 such machines to stitch 60 jerseys?

(A) 8
(B) 12
(C) 16
(D) 18
(E) 20

As a general rule, I think most test-takers make fewer errors when the reason through the problem using English sentences rather than algebraic ones.

9 machines can make 27 jerseys in 4 minutes....so 1 machine can make 3 jerseys in 4 minutes.
We need 4 machines to make 60 jerseys...so we need 1 machine to make 15 jerseys.
15 jerseys is 5x the 3 jerseys that 1 machine can make in 4 minutes, so it's going to take 5x the 4 minutes, which is 20 minutes.

Answer choice E.
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Nine identical machines, each working at the same constant rate, can 04 Jul 2022, 17:39
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ScottTargetTestPrep
Bunuel
Nine identical machines, each working at the same constant rate, can stitch 27 jerseys in 4 minutes. How many minutes would it take 4 such machines to stitch 60 jerseys?

(A) 8
(B) 12
(C) 16
(D) 18
(E) 20

The rate of 9 machines is 27/4. To determine the rate of 4 machines, we can create the proportion:

9/(27/4) = 4/n

36/27 = 4/n

4/3 = 4/n

4n = 12

n = 3

So, it will take 4 machines 60/3 = 20 minutes to stitch 60 jerseys.

Answer: E

ScottTargetTestPrep
Thank you for this helpful explanation.

To clarify, can you divide the rate by the number of machines, keeping constant the amount of work that needs to be done?
For instance, I found that the rate of all 9 machines was equal to (27/4). I then divided the rate by 9 to find the rate of one machine.

So, my work was as follows:
Rate*4=27
R=27/4
R=27/4/9
(27/36)*4*T=60 ---> T=20 minutes.

Thank you for all of your time and help.
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Nine identical machines, each working at the same constant rate, can 07 Jul 2022, 09:21
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Bunuel
Nine identical machines, each working at the same constant rate, can stitch 27 jerseys in 4 minutes. How many minutes would it take 4 such machines to stitch 60 jerseys?

(A) 8
(B) 12
(C) 16
(D) 18
(E) 20

The rate of 9 machines is 27/4. To determine the rate of 4 machines, we can create the proportion:

9/(27/4) = 4/n

36/27 = 4/n

4/3 = 4/n

4n = 12

n = 3

So, it will take 4 machines 60/3 = 20 minutes to stitch 60 jerseys.

Answer: E

ScottTargetTestPrep
Thank you for this helpful explanation.

To clarify, can you divide the rate by the number of machines, keeping constant the amount of work that needs to be done?
For instance, I found that the rate of all 9 machines was equal to (27/4). I then divided the rate by 9 to find the rate of one machine.

So, my work was as follows:
Rate*4=27
R=27/4
R=27/4/9
(27/36)*4*T=60 ---> T=20 minutes.

Thank you for all of your time and help.

That's another perfectly valid way to solve this question. Dividing 27/4 by 9 gives you the rate of one machine, which is 27/36 = 3/4. Multiplying this number by 4 gives you the rate of 4 machines, which is 3 jersey/minute. Letting T represent the number of minutes for 4 machines to stich 60 jerseys, you write the equation 3T = 60, which gives you T = 20 minutes, which is correct.
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Nine identical machines, each working at the same constant rate, can 07 Jul 2022, 20:00
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Thank you so much! You are the best!
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Thank you so much! You are the best!

Sure thing!
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