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

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sun Apr 28, 2019 9:44 am

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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
B) 7
C) 9
D) 14
E) 24

[spoiler]OA=D[/spoiler]

Source: GMAT Paper Tests

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Source: Beat The GMAT — Problem Solving | Sun Apr 28, 2019 9:44 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon Apr 29, 2019 9:32 pm

VJesus12 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
B) 7
C) 9
D) 14
E) 24

[spoiler]OA=D[/spoiler]

Source: GMAT Paper Tests

Given that the first carpenter worked alone for 1 day on a job that would take him 6 more days to finish, the rate of the first carpenter = 1/7

Since 1-day work of the first carpenter is done, the part of work remaining = 1 - 1/7 = 6/7

Again, given that the first carpenter and the second carpenter completed the job in 4 more days, 6/7 part of the work was done by them together.

Both the carpenters , working together, would take 7/6 * 4 = 14/3 days to complete the work

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

Thus,

1-day work of the first carpenter + 1-day work of the second carpenter = 1-day work of both the carpenters

1/7 + 1/b = 1/(14/3)

1/b = 3/14 - 1/7

b = 14 days

The correct answer: D

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8211; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed May 01, 2019 4:16 pm

VJesus12 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
B) 7
C) 9
D) 14
E) 24

[spoiler]OA=D[/spoiler]

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

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by deloitte247 » Fri May 03, 2019 5:53 am

Carpenter A worked alone for 1 day on a job that should take him 60 more days.
Carpenter A finishes the job (alone) in 7 days.
Carpenter B finishes the same job (alone) in x days.

Let's calculate the rate for each of the carpenter;
Carpenter A's rate per day = 1/7
Carpenter B's rate per day = 1/x

So, to complete 1 work,
$$Work=Days\cdot Rate$$
$$1=\left(1\cdot\frac{1}{7}\right)+\left[4\cdot\left(\frac{1}{7}+\frac{1}{x}\right)\right]$$
$$1=\frac{1}{7}+\left[4\cdot\frac{\left(x+7\right)}{7x}\right]$$
$$1=\frac{1}{7}+\frac{4x+28}{7x}$$
$$1=\frac{x+4x+28}{7x}$$
$$7x=5x+28$$
$$2x=28$$
$$x=\frac{28}{2}=14\ \ \ \ \ \left(Option\ D\right)$$

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