Work - Four machines - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

Work - Four machines

Expert replies

yass20015: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Fri Aug 07, 2015 3:06 am; Thanked: 1 times

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 ?
Thanks!

Like this post

Source: Beat The GMAT — Problem Solving | Mon Aug 10, 2015 2:00 pm

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

yass20015: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Fri Aug 07, 2015 3:06 am; Thanked: 1 times

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

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review