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Three machines are operating simultaneously and independently at diffe

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Three machines are operating simultaneously and independently at diffe  [#permalink]

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New post 17 Apr 2017, 01:09
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Question Stats:

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Three machines are operating simultaneously and independently at different rates. Machine A produces 1 widget in 4 minutes, Machine B produces 1 widget in 3 minutes, and Machine C produces 1 widget in 5 minutes. If two machines are to be chosen to make 20 widgets in the shortest possible time, approximately how many minutes will it take to produce 20 widgets?

A. 30
B. 34
C. 36
D. 44
E. 70

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Re: Three machines are operating simultaneously and independently at diffe  [#permalink]

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New post 17 Apr 2017, 02:38
Fastest machines are A and B.

x(1/4 + 1/3) = 20

x = (20 * 12)/7 = 34 mins approx.

Answer: B
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Three machines are operating simultaneously and independently at diffe  [#permalink]

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New post 17 Apr 2017, 05:32
We will choose machine A and B as these two take least time in producing widgets

For producing 10 widgets B will take 30 mins
In those 30 mins we A will produc 30/4= 7.5 widgets

Still need more 2.5 widgets

Lets take take 34 mins now

Machine A will make 34/4 = 8.5 widgets
Machine B will make 34/3 = 11.33 widgets

8.5 + 11.33 = 19.83

Still not 20

So it should be 36 mins

Where both machines together wil make 21 widgets

Ans C

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Re: Three machines are operating simultaneously and independently at diffe  [#permalink]

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New post 17 Apr 2017, 05:38
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Bunuel wrote:
Three machines are operating simultaneously and independently at different rates. Machine A produces 1 widget in 4 minutes, Machine B produces 1 widget in 3 minutes, and Machine C produces 1 widget in 5 minutes. If two machines are to be chosen to make 20 widgets in the shortest possible time, approximately how many minutes will it take to produce 20 widgets?

A. 30
B. 34
C. 36
D. 44
E. 70



..........R.......T......W
A.......1/4.....
B.......1/3
C.......1/5
A+B...7/12...x.....20


T= W/R
T=20/(7/12)
(20*12)/7 = 34.2

Answer : B
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Re: Three machines are operating simultaneously and independently at diffe  [#permalink]

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New post 17 Apr 2017, 12:43
My approach

1/4 + 1/3 = 7/12

7/12 x = 20
x = 34

Answer is B
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Three machines are operating simultaneously and independently at diffe  [#permalink]

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New post 25 Feb 2018, 04:41
Hi Bunuel,

I have one question, It is given in the question that, Machines work simultaneouly but independently.
So can machines share work to produce single widget?

Option B - 34 mins, by 33 mins, Machine A would have produced 8 widgets, Machine B would have produced 11 widgets, now the machines A and B must share producing the last widget to finish by 34 mins approx.

If machines cannot share producing, then answer must be 36 mins..right?

Because, there is similiar problem https://gmatclub.com/forum/crew-a-can-b ... 92819.html
in which, there two crews producing cars, but crews work independently and simulatenously

Can you please help.
thanks
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Re: Three machines are operating simultaneously and independently at diffe  [#permalink]

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New post 25 Feb 2018, 11:13
Always convert everything in terms of rates -
A - 1/4; b = 1/3; C = 1/5
Fastest two - A and B

Overall rate of A and B combined =1/3+1/4 = 7/12 widgets/minutes

So, 7 widgets take 12 mins -
1 widget will take 12/7 mins
so 20 widgets will take - 12/7*20 = 34(approx)
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Re: Three machines are operating simultaneously and independently at diffe  [#permalink]

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New post 22 Jul 2019, 16:14
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Re: Three machines are operating simultaneously and independently at diffe   [#permalink] 22 Jul 2019, 16:14
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