BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Work Rate Problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 8
Joined: Mon Feb 02, 2009 9:21 am

Work Rate Problem

by oxvt » Mon Mar 02, 2009 2:39 am
Working at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

A) 25%
B) 33 1/3%
C) 50%
D) 66 2/3%
E) 75%
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 418
Joined: Wed Jun 11, 2008 5:29 am
Thanked: 65 times

by bluementor » Mon Mar 02, 2009 4:33 am
Machine A seals k cartons in 8 hours
Machine B seals k cartons in 4 hours
Clearly, Machine B is the faster machine here.

For a certain period of time, say 8 hours:

Machine A would have sealed k cartons
Machine B would have sealed 2k kartons

%cartons sealed by B = 2k/(2k+k) = (2/3)*100% = 66 2/3% Choose D.

You will see that this fraction stays the same regardless of time-period you pick.

-BM-
Top
Master | Next Rank: 500 Posts
Posts: 106
Joined: Wed Feb 04, 2009 6:09 am
Location: Louisville, KY
Thanked: 8 times

Re: Work Rate Problem

by marcusking » Mon Mar 02, 2009 5:33 am
oxvt wrote:Working at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

A) 25%
B) 33 1/3%
C) 50%
D) 66 2/3%
E) 75%
Machine A: 1/8
Machine B: 1/4
Total produced: 1/8 + 1/4 => 3/8

Machine B is responsible for 1/4 of the total work completed which we just calculated as 3/8.

(1/4)/(3/8) => (1/4)*(8/3) => 8/12 => 2/3 or 66 2/3%
D.
Top
Master | Next Rank: 500 Posts
Posts: 221
Joined: Wed Jan 21, 2009 10:33 am
Thanked: 12 times
Followed by:1 members

by krisraam » Mon Mar 02, 2009 6:19 am
Same amount of work is done by A in 8hrs
Same amount of work is done by B in 4hrs

Clearly B is faster than A by 100%

If both A and B work for same time. B will end up doing double the work of A.

ie 2/3 of the work = 662/3%

Thanks
raama
Top
Legendary Member
Posts: 941
Joined: Sun Dec 27, 2009 12:28 am
Thanked: 20 times
Followed by:1 members

by bhumika.k.shah » Wed Feb 03, 2010 8:13 am
thanks for the different approaches guys :-)
it really helps coz u may never know which one strikes to u during D day :-)
Top
Master | Next Rank: 500 Posts
Posts: 117
Joined: Wed Jun 09, 2010 7:02 am

by missrochelle » Wed Aug 11, 2010 10:22 am
Quick question here.... sometimes when we are calulating a % of something we multiply them.

16% OF 100 ====> .16 * 100

But here, we divided. 1/4 OF 3/8 ..... instead of multiplying.

Can someone explain why? I got that far, but then multiplied (1/4 times 3/8) so am a bit confused why we are to divide.
Top
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Mon Jul 26, 2010 7:30 pm

by silvi » Mon Feb 14, 2011 10:39 pm
@ missrochelle

the question stated that what percent of the cartons were sealed by the machine working at the faster rate?
it means

cartoons sealed by Machine B / (cartoons sealed by both {Machine A + Machine B}) * 100

so, it's {1/4} / {3/8} * 100 = > 2/3* 100 => 662/3%

Thanks
Silvi
Top
Post new topic Post Reply
• Page 1 of 1