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Work - Four machines

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by yass20015 » Mon Aug 10, 2015 2:00 pm
3 machines operating independently, simultaneously, a,d 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 filled ?
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by Brent@GMATPrepNow » Mon Aug 10, 2015 2:13 pm
Here's the original question:
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
Let's assign some NICE values that satisfy the given conditions.
Let's say that EACH MACHINE produces 1 widget per hour.
So, 3 of the machines working together will produce 3 widgets per hour.

We're told that it takes 36 hour to complete the production order.

Output = (rate)(time)
= (3 widgets per hour)(36 hours)
= 108 widgets
So, the production order = 108 widgets.

IF WE ADD A MACHINE,HOW LONG WILL IT TAKE TO COMPLETE THE ORDER?
Since there are now 4 machines, their COMBINED rate = 4 widgets per hour
time = (output)/(rate)
= (108 widgets)/(4 widgets per hour)
= 27 hours

36 hours - 27 hours = 9 hours
So, it takes 9 fewer hours to complete the order.
Answer: B
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by GMATGuruNY » Mon Aug 10, 2015 2:22 pm
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
Use the following formula:
(machines)(time) = (machines)(time).

Since 3 machines require 36 hours, and 4 machines require x hours, we get:
(3)(36) = (4)(x)
x = 27.

Time decrease = 36-27 = 9 hours.

The correct answer is B.
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by yass20015 » Tue Aug 11, 2015 1:46 am
Thanks. I just found an easy algebric approach:

Lets a: the time needed by each machine to do the work alone.
3 machines need 36h: 1/a + 1/a +1/a = 1/36
we have 3/a = 1/36 so a = 3*36
4 machines need x hours: 4/a = 1/x so x = a/4 = 3*9 = 27

36 - 27 = 9
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