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

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Math Expert
Joined: 02 Sep 2009
Posts: 51197
Nine identical machines, each working at the same constant rate, can  [#permalink]

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02 Jul 2018, 23:04
00:00

Difficulty:

5% (low)

Question Stats:

94% (01:44) correct 6% (01:59) wrong based on 62 sessions

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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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Manager
Joined: 14 Jun 2018
Posts: 220
Re: Nine identical machines, each working at the same constant rate, can  [#permalink]

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03 Jul 2018, 01:26
1
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
Director
Joined: 20 Feb 2015
Posts: 795
Concentration: Strategy, General Management
Re: Nine identical machines, each working at the same constant rate, can  [#permalink]

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03 Jul 2018, 02:31
Bunuel 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

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

9*4/27=4*m*/60
9*60=m*27=20 minutes
Senior SC Moderator
Joined: 22 May 2016
Posts: 2207
Nine identical machines, each working at the same constant rate, can  [#permalink]

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03 Jul 2018, 12:10
Bunuel 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

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

Nine identical machines, each working at the same constant rate, can &nbs [#permalink] 03 Jul 2018, 12:10
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# Nine identical machines, each working at the same constant rate, can

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