A carpenter worked alone for 1 day on a job that...

[AAPL]

A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He an 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.

I don't have clear this PS question.

If carpenter 1 worked for only 1 day on a job that would take him 6 more days, that's mean that this job take him 7 days to complet it, right?

The second carpenter completed the job in 4 more days, I don't understand what can I do to solve it. I appreciate if any expert explain it for me. Thank you so much.

[ErikaPrepScholar]

You're totally right that carpenter 1 would finish the job alone in 7 days. We just need to figure out how to put this information together.

Carpenter 1 works alone at his normal rate for 1 day. His rate is 1 job/7 days, so we have:
$$1\ day\ \cdot\left(\frac{1\ job}{7\ days}\right)$$
Then Carpenter 1 works together with Carpenter 2 for 4 days. They each work at their normal rates. We don't know what Carpenter 2's rate is, so we'll say it's 1 job/x days:
$$4\ days\ \left(\frac{1\ job}{7\ days}+\frac{1\ job}{x\ days}\right)$$
Adding the work done in the first day to the work done in the 4 days should give us 1 full job:
$$1\ day\ \left(\frac{1\ job}{7\ days}\right)+4\ days\ \left(\frac{1\ job}{7\ days}+\frac{1\ job}{x\ days}\right)=1\ job$$
We want to find the number of days it would take Carpenter 2 to finish the job alone, or x. So we'll simply solve for x:
$$1\ \left(\frac{1}{7}\right)+4\left(\frac{1}{7}+\frac{1}{x}\right)=1$$ $$\frac{1}{7}+\frac{4}{7}+\frac{4}{x}=1$$ $$\frac{4}{x}=\frac{2}{7}$$ $$\frac{2}{x}=\frac{1}{7}$$ $$x=14$$
So Carpenter 2 should complete the job alone in 14 days, or answer choice D.

[GMATGuruNY]

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

Let F = the first carpenter and S = the second carpenter.

Since F works for 1 day and would need 6 more days to complete the job, F's time for the whole job = 7 days.
Let the job = the LCM of 7 days and 4 days = 28 units.

Since F takes 7 days to complete the 28-unit job, F's rate = w/t = 28/7 = 4 units per day.
Since F produces 4 units the first day, the remaining work after the first day = 28-4 = 24 units.
Since F and S take 4 days to complete the remaining 24 units, the combined rate for F and S = w/t = 24/4 = 6 units per day.
S's rate = (combined rate for F and S) - (F's rate) = 6-4 = 2 units per day.
Since S's rate is 2 units per day, the time for S alone to complete the 28-unit job = w/r = 28/2 = 14 days.

The correct answer is D.

[Jeff@TargetTestPrep]

A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He an 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 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