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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