GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Nine identical machines, each working at the same constant r
[#permalink]
18 Jun 2018, 14:53
18 Jun 2018, 14:53
Expert Reply
1
Bookmarks
00:00
Question Stats:
95% (01:10) correct
4% (02:08) wrong based on 61 sessions
Hide Show timer Statistics
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
(A) 8
(B) 12
(C) 16
(D) 18
(E) 20
Re: Nine identical machines, each working at the same constant r
[#permalink]
26 Jun 2018, 09:36
26 Jun 2018, 09:36
1
sandy wrote:
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
(A) 8
(B) 12
(C) 16
(D) 18
(E) 20
We know
Work = Rate * *NO. of workers * Time
So work = 27 jerseys
No. of Workers = 9 machine
Time = 4 minutes
therefore we have ;
27 = Rate * 9 * 4
So Rate = \(\frac{3}{4}\) jersey/minute
Now we need to find the time required to make 60 jersey with 4 machine
SO;
Work = Rate * *NO. of workers * Time
Now work = 60 jerseys
Rate = \(\frac{3}{4}\) jersey/minute
No. of workers = 4 machine
Therefore;
60 = \(\frac{3}{4}\) * 4 * Time
or Time = 20 minutes
Re: Nine identical machines, each working at the same constant r
[#permalink]
10 Jul 2018, 05:27
10 Jul 2018, 05:27
Expert Reply
Explanation
To solve a Rates & Work problem with multiple workers, modify the standard formula Work = Rate × Time to this:
Work = Individual Rate × Number of Workers × Time
Solve for an individual machine’s rate, using the fact that 9 machines can stitch 27 jerseys in 4 minutes:
Work = Individual Rate × Number of Workers × Time
27 jerseys = (R)(9)(4 minutes)
R = \(\frac{3}{4}\) jersey per minute
That is, each machine can stitch \(\frac{3}{4}\) of a jersey in 1 minute. Plug that rate back into the formula, but using the details from the second sentence in the problem:
Work = Individual Rate × Number of Workers × Time
\(6 = \frac{3}{4} (4)(T)\)
T = 20
To solve a Rates & Work problem with multiple workers, modify the standard formula Work = Rate × Time to this:
Work = Individual Rate × Number of Workers × Time
Solve for an individual machine’s rate, using the fact that 9 machines can stitch 27 jerseys in 4 minutes:
Work = Individual Rate × Number of Workers × Time
27 jerseys = (R)(9)(4 minutes)
R = \(\frac{3}{4}\) jersey per minute
That is, each machine can stitch \(\frac{3}{4}\) of a jersey in 1 minute. Plug that rate back into the formula, but using the details from the second sentence in the problem:
Work = Individual Rate × Number of Workers × Time
\(6 = \frac{3}{4} (4)(T)\)
T = 20
