Problem Solving

Once the first day is done, 6/7 of the job is left. We then know that the two workers together do 6/7 of a job in 4 days.

So now we know these two things:

Carpenter A does 1 job in 7 days
Carpenters A+B together do 6/7 jobs in 4 days

We can now get the same time for both:

A does 4 jobs in 28 days
A+B do 6 jobs in 28 days

So in 28 days, B must be doing 2 jobs, and thus does 1 job in 14 days.

swerve wrote: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 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

swerve wrote: ↑

Sat Mar 16, 2019 9:36 am

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 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