kspice wrote:

Hello!

I just need help on setting up this work problem:

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

Please include a detailed explanation as to how you arrived at the solution.

Thank you kindly!

~k

This is how I would deal with this problem:

Rate of work of first carpenter = 1/7 work/day

Both, working together, took 4 days to complete (6/7)th of the work.

So they will take 4*7/6 (= 14/3 days) to complete the full work.

Rate of work of both together = 3/14 work/day

Mind you, working alone, first carpenter does 1/7 = 2/14 work/day

Together, they complete 3/14 work/day. So the second carpenter must be doing 1/14 work/day.

So working alone, he will take 14 days.

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Karishma

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