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

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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