It takes Jim N minutes to prepare one omelet. It takes Cole N/2 minute

Question

It takes Jim N minutes to prepare one omelet. It takes Cole N/2 minutes to prepare one omelet. It takes Mitch N/2 minutes to prepare 2 omelets. If Jim, Cole and Mitch together prepare a total of 30 omelets in 40 minutes, then how many minutes would it take Mitch alone to prepare 30 omelets?

A. 70
B. 120
C. 140
D. 160
E. 280

A. 70
B. 120
C. 140
D. 160
E. 280

Scuven · Answer

Jim rate = 1 omelette/N minutes =1/N
C rate = 1 omlette/ (N/2) minutes = 2/N
M rate = 2 omlette/ (N/2) minutes = 4/N

Together they make 30 omlettes in 40 minutes thus 1/N + 2/N + 4/N = 30/40
N= 28/3

Substitute N in M rate and obtain 3 omlettes /7 minutes which is mich rate.

You want to know how much it takes to make 30 omlettes thus multiply both numerator and denominator by 10 
Obtain then 30/70 thus M need 70 minutes to make 30 omlettes

Bunuel · Answer

Cole is twice as fast as Jim and Mitch is 4 times as fast as Jim (it takes Mitch N/2 minutes to prepare 2 omelets, thus N/4 minutes to prepare one omelet).

Say the rate of Jim is x omelet/minute, the rate of Cole 2x omelet/minute, and the rate of Mitch 4x omelet/minute.

Then, from (time)(rate) = (job done):

(40 minutes)(x + 2x + 4x) = (30 omelets);
(40 minutes)(7x) = (30 omelets);

Since it takes 40 minutes to prepare 30 omelets at the rate of 7x omelet/minute, then it would take 40*7/4 = 70 minutes to prepare the same 30 omelets at the rate of 7x*4/7 = 4x omelet/minute (the rate of Mitch).

Or:
(40 minutes)(7x) = (30 omelets);
(40*7/4 minutes)(7x*4/7) = (30 omelets);
(70 minutes)(4x) = (30 omelets);

Answer: A.

Hope it's clear.

It takes Jim N minutes to prepare one omelet. It takes Cole N/2 minute

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GMAT Problem Solving (PS) Questions

It takes Jim N minutes to prepare one omelet. It takes Cole N/2 minute

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