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
A carpenter worked alone for 1 day on a job that would
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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 = 1/7VJesus12 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
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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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
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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,
$$Work=Days\cdot Rate$$
$$1=\left(1\cdot\frac{1}{7}\right)+\left[4\cdot\left(\frac{1}{7}+\frac{1}{x}\right)\right]$$
$$1=\frac{1}{7}+\left[4\cdot\frac{\left(x+7\right)}{7x}\right]$$
$$1=\frac{1}{7}+\frac{4x+28}{7x}$$
$$1=\frac{x+4x+28}{7x}$$
$$7x=5x+28$$
$$2x=28$$
$$x=\frac{28}{2}=14\ \ \ \ \ \left(Option\ D\right)$$
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,
$$Work=Days\cdot Rate$$
$$1=\left(1\cdot\frac{1}{7}\right)+\left[4\cdot\left(\frac{1}{7}+\frac{1}{x}\right)\right]$$
$$1=\frac{1}{7}+\left[4\cdot\frac{\left(x+7\right)}{7x}\right]$$
$$1=\frac{1}{7}+\frac{4x+28}{7x}$$
$$1=\frac{x+4x+28}{7x}$$
$$7x=5x+28$$
$$2x=28$$
$$x=\frac{28}{2}=14\ \ \ \ \ \left(Option\ D\right)$$