A work crew of 4 Men takes 5 days to complete one-half

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

A work crew of 4 Men takes 5 days to complete one-half

by AAPL » Thu Apr 05, 2018 12:39 pm

A work crew of 4 Men takes 5 days to complete one-half of a job. If 6 men are then added to the crew and the men continue to work at the same rate, how many days will it take the enlarged crew to do the rest of the job?

A. 2
B. 3
C. 3 1/3
D. 4
E. 4 4/5

The OA is A.

Suppose 1 man can do the work in X days.

So 4 men will do in,

4/X = 1/5*1/2 as half job is done

X=40

Now 6 more are added then

10/40=1/2*1/d for remaining half job

d=2 Number of days. Option A.

Has anyone another approach to solve this PS question? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Thu Apr 05, 2018 12:39 pm

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by GMATGuruNY » Thu Apr 05, 2018 1:28 pm

AAPL wrote:A work crew of 4 Men takes 5 days to complete one-half of a job. If 6 men are then added to the crew and the men continue to work at the same rate, how many days will it take the enlarged crew to do the rest of the job?

A. 2
B. 3
C. 3 1/3
D. 4
E. 4 4/5

Let the rate for each man = 1 unit per day, implying that the combined rate for 4 men = 4 units per day.
Since the rate for the original 4-men crew = 4 units per day, the amount of work produced in the first 5 days = rt = 4*5 = 20 units.
Since these 20 units constitute 1/2 the job -- implying that the whole job is 40 units -- the remaining work = 20 units.
When 6 men are added -- increasing the total number of men to 10 -- the rate increases to 10 units for day.
Since the rate for the 10-men crew = 10 units per day, the time for the 10-men crew to produce the remaining 20 units = w/r = 20/10 = 2 days.

The correct answer is A.

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TTT

by Jake@ThePrincetonReview » Thu Apr 05, 2018 3:51 pm

Another way to think about this kind of problem (without doing algebra) is to plug in a number of "widgets" to represent the entire job. Since we're working with 4, 5, and 6, let's make the job equal to 120 widgets (a nice multiple of 4, 5, and 6).
Job = 120 Widgets.

Now, you're told that it takes 4 men 5 days to complete half the job, so that's 20 man-days to complete 60 widgets, which would break down to 1 man = 3 widgets/day.

Next, you're asked to calculate how many days it would take to complete the job if we add 6 men.
Completing the job = 60 more widgets
And now we have 10 men, who we know can each complete 3 widgets per day. So that's 30 widgets per day completed by 10 men, and therefore, the 10 men would be able to complete the remaining 60 widgets in 2 days.

Jake Schiff
GMAT Instructor and MasterTrainer