GMAT Challenge Series (700+): Q15

 This question is dedicated to my friend's venture Otto's Burger:  www.ottosburger.com  - congrats Dan!

This question is dedicated to my friend's venture Otto's Burger: www.ottosburger.com - congrats Dan!

Question:

3 cooks have to make 80 burgers. Working together they can make 20 burgers every minute. The 1st cook began working alone and made 20 burgers having worked for sometime more than 3 minutes. The remaining part of the work was done by 2nd and 3rd cook working together. Working in this fashion, it took the 3 cooks a total of 8 minutes to make the 80 burgers. How many minutes would it take the 1st cook alone to cook 160 burgers?

A. 16 minutes

B. 24 minutes

C. 32 minutes

D. 40 minutes

E. 30 minutes

MBA Wisdom's Answer:

$$\text{Let the work rate per minute of the 1st cook be: } \textit{A}$$ $$\text{Let the work rate per minute of the 2nd cook be: } \textit{B}$$ $$\text{Let the work rate per minute of the 3rd cook be: } \textit{C}$$ $$$$ $$\textit{work} = \left(\textit{rate}\right) \left(\textit{time}\right)$$ $$\text{Working together the cooks can make 20 burgers in a minute, therefore:}$$ $$\textit{A} + \textit{B} + \textit{C} = {20}$$ $$$$ $$\text{Let the time that the 1st cook works be: } \textit{t} \text{ where } \textit{ t} > {3}$$ $$\text{The time that the 2nd and 3rd cook work together is: } {8} - \textit{t}$$ $$$$ $$\textit{work of 1st cook} = \left(\textit{A}\right) \left(\textit{t}\right) = {20}$$ $$\textit{work of 2nd cook} = \left(\textit{B}\right) \left({8} - \textit{t}\right)$$ $$\textit{work of 3rd cook} = \left(\textit{C}\right) \left({8} - \textit{t}\right)$$ $$$$ $$\textit{work of 1st cook} + \textit{work of 2nd cook} + \textit{work of 3rd cook} = {80}$$ $$\left(\textit{A}\right) \left(\textit{t}\right) + \left(\textit{B}\right) \left({8} - \textit{t}\right) + \left(\textit{C}\right) \left({8} - \textit{t}\right) = {80}$$ $${4}\textit{A} + {4}\textit{B} + {4}\textit{C} = {80}$$ $$\left(\textit{A}\right) \left(\textit{t}\right) + \left(\textit{B}\right) \left({8} - \textit{t}\right) + \left(\textit{C}\right) \left({8} - \textit{t}\right) = {4}\textit{A} + {4}\textit{B} + {4}\textit{C}$$ $$\textit{t} \text{ must equal 4}$$ $$$$ $$\text{As a result, we know that the 1st cook can make 20 burgers in 4 minutes}$$ $$\text{Multiply this by 8 and we get 160 burgers in 32 minutes}$$

C. 32 minutes