SOLUTION: Twelve men can finish a job in 16 days. Five men were working at the start, after 8 days 3 more men were added. How many days will it take to finish the job?

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Question 765043: Twelve men can finish a job in 16 days. Five men were working at the start, after 8 days 3 more men were added. How many days will it take to finish the job?
Found 2 solutions by ankor@dixie-net.com, josgarithmetic:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Twelve men can finish a job in 16 days.
Five men were working at the start, after 8 days 3 more men were added.
How many days will it take to finish the job?
:
Find the number of man-days required to do the job.
12 * 16 = 192 man-days
:
Let t = days worked after 8 days to complete the job
5(t+8) + 3t = 192
5t + 40 + 3t = 192
8t = 192 - 40
8t - 152
t = 152/8
t = 19 more days required to do the job
:
:
Check this: 5 men worked 19 + 8 = 27 days, 3 worked 19 days
5*27 + 3*19 = 192

Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
1. FIND WORK RATE FOR 1 MAN

12 men do the job in 16 days;
1 man does the job in 16*12 days, or
1 man's rate is highlight%281%2F%2816%2A12%29%29 jobs per day.

2. FORM WORK RATES FOR 5-MAN GROUP AND FOR 8-MAN GROUP

5-man work rate is simply highlight%285%281%2F%2816%2A12%29%29%29 and the 8-man rate is highlight%288%281%2F%2816%2A12%29%29%29

3. SPLIT THE ANALYSIS INTO TWO TIME PHASES:
5 MEN FOR 8 DAYS,
AND
THE 8 MEN FOR SOME DAYS TO FINISH THE JOB.

The actual variable here now is for how many days were necessary to complete the job. The portions of job are added, or summed to be the whole job.
You do the rest of this.