A carpenter worked alone for 1 day on a job that would take

[swerve]

A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 4 more days.
How many days would it have taken the second carpenter to do the complete job working alone?

A. \(4\frac{2}{3}\)
B. \(7\)
C. \(9\)
D. \(14\)
E. \(24\)

The OA is D

Source: GMAT Paper Tests

[Jay@ManhattanReview]

A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 4 more days.
How many days would it have taken the second carpenter to do the complete job working alone?

A. \(4\frac{2}{3}\)
B. \(7\)
C. \(9\)
D. \(14\)
E. \(24\)

The OA is D

Source: GMAT Paper Tests

Given that the first carpenter worked alone for 1 day on the job that would take him 6 more days to finish, working alone, he would take 7 days to finish the work.

Say, working alone, the second carpenter takes b days to finish the work.

As per the question, the first carpenter worked alone for 1 day, and then both the carpenters worked together for 4 days.

Thus, (1/7 + 4/7) + 4/b = 1

=> b = 14 days

The correct answer: D

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 4 more days.
How many days would it have taken the second carpenter to do the complete job working alone?

A. \(4\frac{2}{3}\)
B. \(7\)
C. \(9\)
D. \(14\)
E. \(24\)

The OA is D

Source: GMAT Paper Tests

The rate of the first carpenter is 1/7.

After the first day's work, 1/7 of the job was complete, and so the amount of work remaining to be accomplished was 6/7 of the job. The two men working together completed that remaining work (6/7 of job) in 4 days. Thus, the combined rate of the two carpenters is (6/7)/4 = 6/28 = 3/14.

Let n be the number of days it takes the second carpenter to complete the job by himself. We can create the following equation:

1/7 + 1/n = 3/14

Multiplying by 14n, we have:

2n + 14 = 3n

14 = n

Answer: D

[Brent@GMATPrepNow]

A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 4 more days.
How many days would it have taken the second carpenter to do the complete job working alone?

A. \(4\frac{2}{3}\)
B. \(7\)
C. \(9\)
D. \(14\)
E. \(24\)

The OA is D

Source: GMAT Paper Tests

A straightforward approach is to assign a nice value to the job.
We're looking for a number that works well with the given numbers (7 days to complete the job, and 4 extra days with help).
So let's say the carpentry job consists of making 56 wooden widgets

GIVEN: A carpenter worked alone for 1 day on a job that would take him 6 more days to finish.
This tells us that it would take the carpenter 7 days to make 56 wooden widgets
So, in ONE day, the carpenter can make 8 wooden widgets.
So, after the first day, the number of widgets we still need to make = 56 - 8 = 48

GIVEN: He and another carpenter completed the job in 4 more days.
So the two carpenters we're able to make 48 wooden widgets in 4 days
This means their COMBINED rate is 12 widgets per day
We already know that the FIRST carpenter makes 8 wooden widgets per day
This means the SECOND carpenter can make 4 wooden widgets per day.

QUESTION: How many days would it have taken the second carpenter to do the complete job working alone?
The job consists of making 56 wooden widgets
The SECOND carpenter can make 4 wooden widgets per day

time = output/rate
So, time = 56/4 = 14 days

Answer: D

Cheers,
Brent