Question 3

Explanation

Let's analyze the project conditions before and after workers get sick.

Initial Plan:

The work is planned to be completed by $12$ people in $16$ days. Total workload = $12 \times 16 = 192$ work units.

After 4 Days:

The work has been done for $4$ days by $12$ people. Completed work = $12 \times 4 = 48$ units. Remaining workload = $192 - 48 = 144$ units.

Also, the remaining normal time is $16 - 4 = 12$ days if done by $12$ people.

Changed Condition:

There are $4$ sick people, so the remaining workers are $12 - 4 = 8$ people. We use inverse proportion to find the additional time ($w$) needed by $8$ people to complete the remaining work.

So, $8$ workers need $18$ more days to complete the remaining project.

The total project completion time is the time already elapsed plus the remaining time needed.

So, the project can be completed in $22$ days.