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

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