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# A machine puts c caps on bottles in m minutes. How many hours will it

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Math Expert
Joined: 02 Sep 2009
Posts: 49968
A machine puts c caps on bottles in m minutes. How many hours will it  [#permalink]

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16 May 2016, 02:45
10
00:00

Difficulty:

55% (hard)

Question Stats:

61% (01:22) correct 39% (01:53) wrong based on 326 sessions

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A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles?

A. 60bm/c
B. bm/(60c)
C. bc/(60m)
D. 60b/(cm)
E. b/(60cm)

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Joined: 12 Jun 2015
Posts: 79
Re: A machine puts c caps on bottles in m minutes. How many hours will it  [#permalink]

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16 May 2016, 03:05
3
A machine puts c caps on bottles in m minutes.
So, the machine puts 1 cap in m/c minutes

To put caps on b bottles, the machine will take bm/c minutes
In order to calculate the no. of hours taken , divide the product by 60.

Intern
Joined: 06 May 2016
Posts: 16
WE: Education (Education)
Re: A machine puts c caps on bottles in m minutes. How many hours will it  [#permalink]

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16 May 2016, 05:27
1
The key for me is to realise that 1 bottle can only have 1 cap.
(ie bottles can be multiplied with minutes/cap and cancel out leaving only time)

Without that it seems super difficult but actually is a very straightforward calculation.
SVP
Joined: 26 Mar 2013
Posts: 1836
Re: A machine puts c caps on bottles in m minutes. How many hours will it  [#permalink]

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17 May 2016, 05:23
We can plug in simple numbers

2 caps per 1 min,, then rate= 2 caper/min

Put b= 120 or 60 bottles.. I used 120 bottles

120= 2 * t.....>t=60 min =1 hr

Scanning the answer choice.. Eliminate A & D as you need to divide minute by 60.
Eliminate E as CM should be together.

Substitute number in choice B & C

In bm/60c= (120*1)/ (2 *60) = 1

Manager
Joined: 01 Nov 2016
Posts: 67
Concentration: Technology, Operations
Re: A machine puts c caps on bottles in m minutes. How many hours will it  [#permalink]

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24 Apr 2017, 15:07
Bunuel wrote:
A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles?

A. 60bm/c
B. bm/60c
C. bc/60m
D. 60b/cm
E. b/60cm

A machine puts c caps on bottles in M minutes. A bottle can only have 1 cap, so this means that in M minutes, the machine will cap C bottles

$$\frac{M minutes}{C bottles}$$

How many hours will it take to put caps on B bottles? This is a comparison ratio:

$$\frac{M minute}{C bottles}$$ * $$\frac{1 hour}{60 minutes}$$ = $$\frac{X hours}{B bottles}$$

This becomes:

$$\frac{(M minute)(B bottles)(1 hour)}{(C bottles)(60 minutes)}$$ = $$x hours$$

Simplify to:

$$\frac{mb}{60c}$$ = $$x hours$$

This question's only difficulty is seeing that they want you to do a comparison between c bottles and b bottles. They intentionally made the letters confusing for those that could only see b should stand for bottles.
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Re: A machine puts c caps on bottles in m minutes. How many hours will it  [#permalink]

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22 May 2017, 15:43
2
2
my approach
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Manager
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Re: A machine puts c caps on bottles in m minutes. How many hours will it  [#permalink]

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20 Sep 2017, 10:37
W2*T1=W1*T2

Always works. Just switch the work and Keep all other factors on the same side.
Manager
Joined: 22 Nov 2016
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Location: United States
GPA: 3.4
Re: A machine puts c caps on bottles in m minutes. How many hours will it  [#permalink]

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09 Nov 2017, 13:39
c caps in m minutes.
Hence, in 1 hour, the machine puts $$\frac{60c}{m}$$ caps. This is the rate.
Work is given as b.

$$W=b ; R=\frac{60c}{m} ; T=?$$

$$T= \frac{W}{R} = \frac{b*m}{60c}$$
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Manager
Joined: 02 Jan 2016
Posts: 102
A machine puts c caps on bottles in m minutes. How many hours will it  [#permalink]

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03 Aug 2018, 21:35
Rate Time = Work
C/M M C

C/M x = B

So, (RT = W); X*C/M = B; BM/C this is in Hours, therefore BM/C/60= BM/C60
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Re: A machine puts c caps on bottles in m minutes. How many hours will it  [#permalink]

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03 Aug 2018, 21:59
Bunuel wrote:
A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles?

A. 60bm/c
B. bm/(60c)
C. bc/(60m)
D. 60b/(cm)
E. b/(60cm)

my approach:

we have : c caps --> m minutes
therefore b caps --> $$\frac{(b*m)}{c}$$ minutes

And : 60 minutes = 1 hour
so: $$\frac{(b*m)}{c}$$ minutes = $$\frac{(b*m)}{(c*60)}$$ hours

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Re: A machine puts c caps on bottles in m minutes. How many hours will it &nbs [#permalink] 03 Aug 2018, 21:59
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