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

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Veritas Prep GMAT Instructor
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Re: 3 cooks have to make 80 burgers.They are known to make 20 [#permalink]  18 Feb 2014, 20:22
Expert's post
prasannajeet wrote:
Hi Karishma
I am little wore out by looking long solution...
Just let me know whether my procedure is right or wrong???

Lets the time taken by 3 cooks are A hr,B hr,C hr
So there rate is 1/A+1/B+1/C=1/20..

Now as per the question 1st cook taken little more time than 3 min...
If i consider cook 1 will take exactly 3 min then 1/A*3=20 so we get 1/A=20/3...
So to make 160 burgers it will take 160/20/3(because W/R=T)=24 min but as per the question it takes LITTLE more than 3 min so answer must be 32.....

Rgds
Prasnnajeet

The sum of the rates is 20 burgers/min.
1/A+1/B+1/C= 20
Though why you would assume time rather than rate itself to get a much neater equation: A + B + C = 20, I am not sure.

Also, all you are saying is that A takes more than 3 mins for 20 burgers so he will take more than 8*3 mins for 8*20 burgers. What if you have options 28, 30, 32 and 34. How do you say how much is '(sometime)*8 more than 24 mins'?
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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Intern Joined: 27 Jan 2014 Posts: 6 Location: India Concentration: General Management, Finance Schools: HBS '16, Wharton '16 GMAT Date: 04-25-2014 GPA: 3.77 WE: Project Management (Investment Banking) Followers: 0 Kudos [?]: 8 [1] , given: 6 Re: 3 cooks have to make 80 burgers.They are known to make 20 [#permalink] 19 Feb 2014, 20:41 1 This post received KUDOS Although many answer explanations have been given above, but since mine was different - thought to share this perspective with the group. I am using a simple quadratic equation to solve. It is given that A takes sometime more than 3 minutes to make 20 burgers, let us say that he takes 3+x minutes. ------ (1) Also is given that together A, B and C take 8 minutes to make 80 burgers (therefore B and C together make 60 burgers in {8 - (3+x)} mins. or (5-x) mins) ------- (2) Also given that A, B, C make 20 burgers per minute, all working together. ------ (3) In 1 min, A alone can make 20/(3+x) burgers, ------ (4) In 1 min, B+C can together make 60/(5-x) burgers ------ (5) Combining statements (3), (4) and (5), 20/(3+x) + 60/(5-x) = 20 Simplifying, we get, 1/(3+x) + 3/(5-x) = 1 or x^2 - 1 = 0 => x = 1 or -1 Since A's time is more than 3, therefore it cannot be -1. Hence x = 1. Therefore, A takes 3+x = 3+1 = 4 mins to make 20 burgers => 4*8 = 32 mins to make 160 burgers. virtualanimosity wrote: 3 cooks have to make 80 burgers.They are known to make 20 pieces every minute working together.The 1st cook began workin alone and made 20 pieces having worked for sometime more than 3 mins.The remaining part of the work was done by second and 3rd cook working together.It took a total of 8 minutes to complete the 80 burgers.How many minutes would it take the 1st cook alone to cook 160 burgers? A. 16 minutes B. 24 mins C. 32 mins D. 40 mins E. 30 mins Intern Joined: 14 Apr 2014 Posts: 3 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: 3 cooks have to make 80 burgers.They are known to make 20 [#permalink] 15 Apr 2014, 09:17 virtualanimosity wrote: 3 cooks have to make 80 burgers.They are known to make 20 pieces every minute working together.The 1st cook began workin alone and made 20 pieces having worked for sometime more than 3 mins.The remaining part of the work was done by second and 3rd cook working together.It took a total of 8 minutes to complete the 80 burgers. How many minutes would it take the 1st cook alone to cook 160 burgers? A. 16 minutes B. 24 mins C. 32 mins D. 40 mins E. 30 mins To me it is simply stating, if cook one was to continue cooking at a rate of 20 burgers >3mins, how long would it take to cook 160 burgers? basic assumption being it was 4 mins so 5 burgers a minute (20/4) then 160/5 = 32 minutes cook time. Might be way too simplistic a solution but with the time constraints of the exam some element of rational judgement must be made, no? Interpretation of the quetion is key here I guess. Intern Joined: 22 Nov 2012 Posts: 15 Location: United States Concentration: Statistics, Technology WE: Information Technology (Consumer Products) Followers: 0 Kudos [?]: 6 [0], given: 11 Re: 3 cooks have to make 80 burgers.They are known to make 20 [#permalink] 15 Apr 2014, 10:14 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! Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4687 Location: Pune, India Followers: 1079 Kudos [?]: 4841 [1] , given: 163 Re: 3 cooks have to make 80 burgers.They are known to make 20 [#permalink] 15 Apr 2014, 19:23 1 This post received KUDOS Expert's post 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 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Re: 3 cooks have to make 80 burgers.They are known to make 20   [#permalink] 15 Apr 2014, 19:23
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