Work problem

Expert replies

crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pmFollowed by: 1 member; Thanked: 15 times; GMAT Score:690

by crackgmat007 » Wed May 06, 2009 9:38 am

Q: Working alone at its constant rate, machine K took 3 hours to produce 1/4of the units produced
last Friday. Then machine M started working and the two machines, working simultaneously at
their respective constant rates, took 6 hours to produce the rest of the units produced last Friday.
How many hours would it have taken machine M, working alone at its constant rate, to produce all
of the units produced last Friday?
A. 8
B. 12
C. 16
D. 24
E. 30

OA – D

Total hours of work is 12 (1/4 is 3 hours, hence 1 is 12 hours). Balance work is 9 hours, which is completed by M & K in 6 hours. Can someone explain how do I go from here?

Source: Beat The GMAT — Problem Solving | Wed May 06, 2009 9:38 am

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Wed May 06, 2009 10:12 am

You're almost there.

Since it took machine K 3 hours to complete 1/4 of the job, it would indeed take it 12 hours to do it alone.
Since it took both machines 6 hours to complete the remaining 3/4 of the job, it would take them both 4/3 * 6 = 8 hours to complete the whole thing.

Now all you need to do is apply that "work formula"

1/k + 1/m = 1/(mk) - where k = time it takes k to complete the job alone; m = time it takes m to complete the job alone; mk = time it takes both machines to do the job working together.

1/12 + 1/m = 1/8

1/m = 1/8 - 1/12 = 1/24 ------------ m = 24.

crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pmFollowed by: 1 member; Thanked: 15 times; GMAT Score:690

by crackgmat007 » Wed May 06, 2009 11:10 am

got it...thanks much

Bhattu: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Thu Apr 05, 2007 4:58 am; Thanked: 2 times; GMAT Score:600

by Bhattu » Fri May 08, 2009 4:20 am

I went a bit more basic on this.

K took 3 hrs to do 1/4 of the job, then K took 6 hrs to do 1/2 the job. Therefore K did 3/4 of the work in 9 Hrs and M did 1/4 of the work in 6 hrs.

If M did 1/4 in 6hrs, it would take M 6*4 hours to complete the job.

I would go for the earlier solution as it sticks to the tried and tested formula for work problems

Featured schoolRound 2 closes Jan 7, 2027 54 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 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