SOLUTION: A commercial building was built in 1 - 7/8 months by 20 skilled workers and 30 unskilled laborers. If 30 skilled men were contracted the group alone would have erected the facility

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Question 226385: A commercial building was built in 1 - 7/8 months by 20 skilled workers and 30 unskilled laborers. If 30 skilled men were contracted the group alone would have erected the facility in 2 months time, How long should it take one unskilled worker alone to complete the job?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A commercial building was built in 1 - 7/8 months by 20 skilled workers and 30 unskilled laborers.
If 30 skilled men were contracted the group alone would have erected the facility in 2 months time,
How long should it take one unskilled worker alone to complete the job?
Find the time required by one skilled worker
:
It says, "Two months with 30 skilled workers only"
that's 60 man/months (skilled) to complete the job
Therefore one man requires 60 months to do the job
:
Then 20 skilled men: 60/20 = 3 months to do the same job
:
:
Change 17%2F8 to 1.875 months
Let u = the time required by 30 unskilled workers
:
Let the completed job = 1
:
Skilled + unskilled = completed job
1.875%2F3 + 1.875%2Fu = 1
:
Multiply equation by 3u
1.875u + 3(1.875) = 3u
5.625 = 3u - 1.875u
5.625 = 1.125u
u = 5.625%2F1.125
:
u = 5 months using 30 unskilled men
therefore
5*30 = 150 man/months (unskilled) to do the job
therefore:
150 months for one unskilled man to do the job
and
60 months for one skilled man to do it
;
:
Check solution:
1.875%2F3 + 1.875%2F5 = 1
.625 + .375 = 1