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Nine identical machines, each working at the same constant r

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GMAT Club Legend
GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1650 [0], given: 396

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Nine identical machines, each working at the same constant r [#permalink] New post 18 Jun 2018, 14:53
Expert's post
00:00

Question Stats:

87% (01:31) correct 12% (00:00) wrong based on 8 sessions
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
[Reveal] Spoiler: OA

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Sandy
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Director
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Re: Nine identical machines, each working at the same constant r [#permalink] New post 26 Jun 2018, 09:36
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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


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
_________________

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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1650 [0], given: 396

CAT Tests
Re: Nine identical machines, each working at the same constant r [#permalink] New post 10 Jul 2018, 05:27
Expert's post
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
_________________

Sandy
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Re: Nine identical machines, each working at the same constant r   [#permalink] 10 Jul 2018, 05:27
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