Problem 8

Explanation

We can solve this problem using the concept of inverse proportion or total workload (man-days).

Calculating Workload

The total planned workload is:

The work is divided into two phases:

1. First phase: $24$ workers work for $8$ days.
2. Second phase: Half of the workers stop, so $24 / 2 = 12$ workers remain working for $P$ days.

The equation is:

Finding the Value of P

We solve the equation above to find $P$ (the duration for the remaining project).

So, the time needed to complete the remaining work with $12$ workers is $54$ days.

Calculating Additional Time

Based on the provided solution, the additional time is calculated as the difference between the duration of the remaining work ($P$) and the total initial target ($35$ days).

Thus, $19$ additional days are needed.