Answer:
<em>8 more men are needed to complete the job</em>
Step-by-step explanation:
<u>Proportions</u>
This problem can be solved by step-by-step reasoning applying proportions:
- 16 men working 9 hrs a day complete the job in 14 days
- 16 men working 1 hr a day complete the job in 14*9 days
The above statement stands because the fewer hours of work, the more time the job needs to be completed. Let's continue.
- 1 man working 1 hr a day complete the job in 14*9*16 days
The same reasoning applies here, fewer men=more days.
Now for the second condition. Increase the hours/day:
- 1 man working 7 hrs a day complete the job in 14*9*16/7 days
More hours/day=less days to complete the job
- x men working 7 hrs a day complete the job in 14*9*16/(7*x) days
We know this last time is 12 days, thus:
Solving for x:
24 men are needed now, this is an increase of 24-16=8 more men
8 more men are needed to complete the job