Three machines operating independently, simultaneously,

Hi Vincen,

We're told that 3 machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. We're asked if one additional machine were used under the same operating conditions, in how many FEWER hours of simultaneous operation could the production order be fulfilled.

In these types of Work questions, it helps to determine how much work-time is needed to complete the job. Here, we have 3 machines working 36 hours each...

(3 machines)(36 hours each) = 108 machine-hours of work needed to complete the job.

Adding 1 additional machine creates the following equation:

(4 machines)(X hours each) = 108 machine-hours of work
X = 108/4 = 27 hours for each machine

The question asks for how many FEWER hours are needed... 36 hours - 27 hours = 9 fewer hours

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Vincen wrote:Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?

A. 6
B. 9
C. 12
D. 27
E. 48

The OA is B.

I made some calculus and I got 27. Experts, may you show me how to solve this PS question? Thanks.

If 3 machines working together take 36 hours to complete a job, then 1 machine by itself will take 3 times as long, or 3 x 36 = 108 hours to complete the same job. However, 4 machines working together will take ¼ as long, or ¼ x 108 = 27 hours to complete the job. Therefore, 1 additional machine (added to 3 machines) will save 36 - 27 = 9 hours.

Answer: B