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# Running at the same constant rate, 6 identical machines can

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Math Expert
Joined: 02 Sep 2009
Posts: 60625
Running at the same constant rate, 6 identical machines can  [#permalink]

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20 Aug 2012, 03:05
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5% (low)

Question Stats:

94% (01:19) correct 6% (01:43) wrong based on 1680 sessions

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Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

(A) 648
(B) 1,800
(C) 2,700
(D) 10,800
(E) 64,800

Practice Questions
Question: 23
Page: 155
Difficulty: 600

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Re: Running at the same constant rate, 6 identical machines can  [#permalink]

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20 Aug 2012, 03:05
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SOLUTION

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

(A) 648
(B) 1,800
(C) 2,700
(D) 10,800
(E) 64,800

6 machines produce 270 bottles per minute;
1 machine produces 270/6=45 bottles per minute;
10 machines produce 45*10=450 bottles per minute;

In 4 minutes 10 machines produce 450*4=1,800 bottles.

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Re: Running at the same constant rate, 6 identical machines can  [#permalink]

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20 Aug 2012, 08:30
Ans=(270*10*4)/(6)
=1800

option B.
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Re: Running at the same constant rate, 6 identical machines can  [#permalink]

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20 Aug 2012, 09:52
Each machine can produce (270/6) = 45 bottles per minute

45 * 10 = 450 bottles per minute

450 * 4 = 1800 bottles in 4 minutes.
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Re: Running at the same constant rate, 6 identical machines can  [#permalink]

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12 Apr 2013, 10:11
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Let's take the approach that uses the answer choices to eliminate wasted time.

270/6 is a little less than 300/60 = 50 bottles per minute per machine. 10 machines = 500 per minute. 4 minutes worth = 2000 bottles as being slightly HIGHER than the answer we need.

Looking at the answers it is clear...we can only choose (B) 1800 bottles starting with an upper bound of 2000.
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Running at the same constant rate, 6 identical machines can prod  [#permalink]

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22 Apr 2013, 18:33
270/6 = 45 BPM X 10 Machines = 450 BPM X 4 MIN = 1,800.

Kudos if this is easier!
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Re: Running at the same constant rate, 6 identical machines can  [#permalink]

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10 Sep 2014, 01:08
Bunuel wrote:
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

(A) 648
(B) 1,800
(C) 2,700
(D) 10,800
(E) 64,800

Practice Questions
Question: 23
Page: 155
Difficulty: 600

6 identical machine produce 270bottles/min then 1machine - 45bottles/min

10 machine - 450 bottles/min

for 4 minutes--> 1800
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Re: Running at the same constant rate, 6 identical machines can  [#permalink]

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15 Nov 2014, 21:52
better as fractions:

270*10/6*4/1=1800

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Re: Running at the same constant rate, 6 identical machines can  [#permalink]

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20 Nov 2014, 01:59

Equation would be

$$= \frac{270}{6} * 10 * 4 = 1800$$
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Re: Running at the same constant rate, 6 identical machines can  [#permalink]

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25 May 2016, 07:11
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Bunuel wrote:
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

(A) 648
(B) 1,800
(C) 2,700
(D) 10,800
(E) 64,800

To solve this problem, we first want to determine the rate of each machine. Since each machine works at the same constant rate, each machine’s rate is 270/6 = 45 bottles per minute. Now since there are 10 such machines, the rate of the 10 machines together is 10 x 45 = 450 bottles per minute.

Finally, we are asked to determine the number of bottles these 10 machines can produce in 4 minutes. Thus:

rate x time = work

450 x 4 = 1,800 bottles

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Re: Running at the same constant rate, 6 identical machines can  [#permalink]

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25 May 2016, 08:55
Bunuel wrote:
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

(A) 648
(B) 1,800
(C) 2,700
(D) 10,800
(E) 64,800

Practice Questions
Question: 23
Page: 155
Difficulty: 600

6 machines can produce 270 bottles, so 10 machines can produce 270*10/6

This can be produced in 1 minute. Total bottles that can be produced in 4 minutes :-
270*10*4/6= 1800 bottles

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Re: Running at the same constant rate, 6 identical machines can  [#permalink]

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05 Jul 2016, 05:04
Bunuel wrote:
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

(A) 648
(B) 1,800
(C) 2,700
(D) 10,800
(E) 64,800

Practice Questions
Question: 23
Page: 155
Difficulty: 600

r*t=w
we have 6 machine here so

6*(r*1)=270
r*1=45===> r=45

r*t=w

we got 10 machine
10*(r*t)=w
10*(45*4)=1800

t was 4 according to the question
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Re: Running at the same constant rate, 6 identical machines can  [#permalink]

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26 Jun 2017, 16:52

Looking at the answer choices we can approximate and save a lot of time

Rate of each bottle $$= \frac{270}{6}$$ = This is somewhere between 40 and 50 bottles per minute

10 bottles will produce between 400 and 500 bottles per minute
in 4 minutes the same 10 bottles will produce between 1600 and 2000 bottles.

The only answer that lies in this range is B
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Re: Running at the same constant rate, 6 identical machines can  [#permalink]

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07 Dec 2017, 15:09
1
Hi All,

We're told that 6 identical machines can produce a total of 270 bottles per minute. We're asked for the number of bottles that 10 such machines would produce in 4 minutes when working at this same rate.

Since this is just a big 'rate' question, you can approach the math in a couple of different ways. From the information in the first sentence, since 6 divides evenly into 270, you could figure out the rate/minute for 1 machine...

270/6 = 45 bottles/minute for 1 machine

Since we have 10 machines working for 4 minutes each, that would give us...

(10)(4)(45) = 1800 bottles

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Re: Running at the same constant rate, 6 identical machines can  [#permalink]

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31 Jan 2019, 02:54
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Re: Running at the same constant rate, 6 identical machines can   [#permalink] 31 Jan 2019, 02:54
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