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Working alone at its own constant rate, a machine seals k cartoons in

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Working alone at its own constant rate, a machine seals k cartoons in [#permalink]

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New post 05 Nov 2011, 13:20
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Working alone at its own constant rate, a machine seals k cartoons in 8 hours, and working at its own constant rate a second machine seals k cartoons in 4 hours. if 2 machines each working at its own constant rate and for the same period of time together sealed a certain no of cartoons. what percentage of the cartoons were sealed by the machine working at the faster rate?

A. 25%
B. 33 1/3%
C. 50%
D. 66 2/3%
E. 75%

[Reveal] Spoiler:
Can someone please tell me whether I have done this correctly as answer is not given?

Sol : Let say k =32

Rate of 1st machine = 32/8 = 4 cartons/hr
Rate of 2nd machine = 32/4 = 8 cartons/hr

%ge of cartons sealed by 2nd machine = 8/32*100= 25%


OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/working-alon ... 04981.html
[Reveal] Spoiler: OA

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Re: Working alone at its own constant rate, a machine seals k cartoons in [#permalink]

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New post 05 Nov 2011, 14:10
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enigma123 wrote:
Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own
constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own
constant rate and for the same period of time, together sealed a certain number of cartons, what percent of
the cartons were sealed by the machine working at the faster rate?

Can someone please tell me whether I have done this correctly as answer is not given?

Sol : Let say k =32

Rate of 1st machine = 32/8 = 4 cartons/hr
Rate of 2nd machine = 32/4 = 8 cartons/hr

%ge of cartons sealed by 2nd machine = 8/32*100= 25%



The best way to solve this question is to freeze the number of cartons generated at a perticular time, Say after 8 hrs.

For example - if i calculate the total number of cartons generated after 8 hours -
total number of cartons generated after 8 hours from 1st Machine = k cartons
total number of cartons generated after 8 hours from 2nd Machine = 2k cartons

Obviously, machine working at the faster rate is 2nd machine. hence, 2k/3k = 66.66%

You can try this with 4 hrs and 16 hours also.

Hope it helps.
Cheers!
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Re: Working alone at its own constant rate, a machine seals k cartoons in [#permalink]

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New post 05 Nov 2011, 14:12
enigma123 wrote:
Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own
constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own
constant rate and for the same period of time, together sealed a certain number of cartons, what percent of
the cartons were sealed by the machine working at the faster rate?

Can someone please tell me whether I have done this correctly as answer is not given?

Sol : Let say k =32

Rate of 1st machine = 32/8 = 4 cartons/hr
Rate of 2nd machine = 32/4 = 8 cartons/hr

%ge of cartons sealed by 2nd machine = 8/32*100= 25%




You have assumed that Machine 1 and 2 are not sealing k cartons (32 in your case) at the same time.
Machine 1 will take more time to seal k cartons as its rate (k/8) is less than that of machine 2 (k/4).

Now since both are working for the same time lets say 1 hour, they together seal 8+4=12 cartons and not 32.
So, %ge of cartons sealed by 2nd machine = 8/12*100 = 66.66%.

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Re: Working alone at its own constant rate, a machine seals k cartoons in [#permalink]

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New post 14 Aug 2017, 22:15
enigma123 wrote:
Working alone at its own constant rate, a machine seals k cartoons in 8 hours, and working at its own constant rate a second machine seals k cartoons in 4 hours. if 2 machines each working at its own constant rate and for the same period of time together sealed a certain no of cartoons. what percentage of the cartoons were sealed by the machine working at the faster rate?

A. 25%
B. 33 1/3%
C. 50%
D. 66 2/3%
E. 75%

[Reveal] Spoiler:
Can someone please tell me whether I have done this correctly as answer is not given?

Sol : Let say k =32

Rate of 1st machine = 32/8 = 4 cartons/hr
Rate of 2nd machine = 32/4 = 8 cartons/hr

%ge of cartons sealed by 2nd machine = 8/32*100= 25%




As second one works twice as fast as the first, working together second will do 2/3 of work and the first 1/3 of work (their ratio 1/2).

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/working-alon ... 04981.html
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Re: Working alone at its own constant rate, a machine seals k cartoons in   [#permalink] 14 Aug 2017, 22:15
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