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

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Joined: 02 Sep 2009
Posts: 49251
Nine identical machines, each working at the same constant rate, can  [#permalink]

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New post 03 Jul 2018, 00:04
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  5% (low)

Question Stats:

94% (01:28) correct 6% (02:28) wrong based on 53 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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Re: Nine identical machines, each working at the same constant rate, can  [#permalink]

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New post 03 Jul 2018, 02:26
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
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Re: Nine identical machines, each working at the same constant rate, can  [#permalink]

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New post 03 Jul 2018, 03:31
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
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Nine identical machines, each working at the same constant rate, can  [#permalink]

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New post 03 Jul 2018, 13:10
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

Answer E
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Nine identical machines, each working at the same constant rate, can &nbs [#permalink] 03 Jul 2018, 13:10
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