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3 cooks have to make 80 burgers.They are known to make 20

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Re: 3 cooks have to make 80 burgers.They are known to make 20 [#permalink] New post 15 Apr 2014, 19:23
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Armada0023 wrote:
VeritasPrepKarishma wrote:
We know that the three together cook 20 burgers in 1 min i.e. we have their combined rate:
ra + rb + rc = 20 burgers/min

Also, they made 80 burgers in 8 mins such that:
\frac{20}{ra} + \frac{60}{(rb + rc)} = 8


Hi Karishma,
Thank you for the wonderful explanation. But, I do get lost when trying to follow how you were able to derive the above equation. Could you walk me through how you were able to set up: \frac{20}{ra} + \frac{60}{(rb + rc)} = 8?

Thank you!


Note that the basic work-rate-time equation is Work = Rate*Time
or Time = Work/Rate

"The 1st cook began working alone and made 20 pieces having worked for sometime more than 3 mins."
If rate of work of first cook = ra, time taken by him to make first 20 burgers = Work/Rate = 20/ra (the work done is 20 burgers were made)

"The remaining part of the work was done by second and 3rd cook working together"
Rates of work of second and third cooks are rb and rc.

Time taken by them together to make next 60 burgers = 60/(ra + rb) (the combined rate of second and third cooks is rb + rc. Rates are additive. You can simply add the rates to get the combined rate)

Time taken to complete making the 80 burgers = 20/ra + 60/(ra + rb)

This is given as 8 so 20/ra + 60/(ra + rb) = 8
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Re: 3 cooks have to make 80 burgers.They are known to make 20 [#permalink] New post 14 Sep 2014, 05:48
Am I the only one who thinks this question can be solved only with this part of information:

Quote:
3 cooks have to make 80 burgers.They are known to make 20 pieces every minute working together.The 1st cook began working alone and made 20 pieces having worked for sometime more than 3 mins.


Some time more than 3 mins ~ 4 minutes

Rate x Time = Work
Rate x 4 = 20
Rate = 5

Now let's solve for 160 burgers:

Rate x Time = Work
5 x Time = 160
Time = 32minutes

Please let me know if doing it like this is somehow wrong.
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Re: 3 cooks have to make 80 burgers.They are known to make 20 [#permalink] New post 14 Sep 2014, 23:31
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iaratul wrote:
Am I the only one who thinks this question can be solved only with this part of information:

Quote:
3 cooks have to make 80 burgers.They are known to make 20 pieces every minute working together.The 1st cook began working alone and made 20 pieces having worked for sometime more than 3 mins.


Some time more than 3 mins ~ 4 minutes

Rate x Time = Work
Rate x 4 = 20
Rate = 5

Now let's solve for 160 burgers:

Rate x Time = Work
5 x Time = 160
Time = 32minutes

Please let me know if doing it like this is somehow wrong.


How does "some time more than 3 mins" imply 4 mins? It could imply 3 mins 2 sec (which is basically 3 mins) or 5 mins or 10 mins etc
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Re: 3 cooks have to make 80 burgers.They are known to make 20 [#permalink] New post 14 Sep 2014, 23:49
Karishma, it's logical of you to ask that question - but I seriously wasn't thinking about that.

I found the question to be extremely difficult and tried to use intuition, instead of any other method. I used the word "Some time" to be very close to 3 minutes, but not close enough to be 3min 2secs. I tried with 3min 30 and 4 mins and found out that I was right. I guess I was employing a dangerous strategy, but I would not have been able to answer the question in under 2 minutes if I didn't do that.

I require more practice :)
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Re: 3 cooks have to make 80 burgers.They are known to make 20 [#permalink] New post 19 Sep 2014, 10:07
Hi Bunuel
Can you please share links to problems similar to this.
I feel these kind of problems test the very concept of time and work.

Thanks in advance
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Re: 3 cooks have to make 80 burgers.They are known to make 20 [#permalink] New post 20 Sep 2014, 11:20
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alphonsa wrote:
Hi Bunuel
Can you please share links to problems similar to this.
I feel these kind of problems test the very concept of time and work.

Thanks in advance


Similar questions to practice:
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a-contractor-estimated-that-his-10-man-crew-could-complete-t-107546.html
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Hope this helps.
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Re: 3 cooks have to make 80 burgers.They are known to make 20   [#permalink] 20 Sep 2014, 11:20
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