Nine identical machines, each working at the same constant rate, can

Question

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

pandeyashwin · Answer

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

CounterSniper · Answer

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

9*4/27=4*m*/60
9*60=m*27=20 minutes

generis · Answer

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

ScottTargetTestPrep · Answer

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

ThatDudeKnows · Answer

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.

woohoo921 · Answer

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.

ScottTargetTestPrep · Answer

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.

woohoo921 · Answer

ScottTargetTestPrep 
Thank you so much! You are the best!

ScottTargetTestPrep · Answer

Sure thing!

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Nine identical machines, each working at the same constant rate, can

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Nine identical machines, each working at the same constant rate, can

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards