To determine how many days it will take for 25 workers to build 25 walls, let's follow a structured approach:
1. Understand the given data:
- 50 workers can build 50 walls in 25 days.
2. Determine the wall-building rate:
- Calculate how many walls one worker can build in one day.
- Since 50 workers can build 50 walls in 25 days, we first find the total work done.
[tex]\[
\text{Total work done by 50 workers in 25 days} = 50 \text{ walls}
\][/tex]
- Converting this to work done per worker per day:
[tex]\[
\text{Rate} = \frac{\text{Total walls}}{\text{Number of workers} \times \text{Number of days}} = \frac{50 \text{ walls}}{50 \text{ workers} \times 25 \text{ days}} = 0.04 \text{ walls per worker per day}
\][/tex]
3. Calculate the total amount of work needed for the new scenario:
- We need 25 workers to build 25 walls.
- The total work required is the same as the number of walls since each wall represents 1 "wall-day" of work.
[tex]\[
\text{Total work (in wall-days)} = 25 \text{ walls}
\][/tex]
- To understand the total work required with the same conditions:
[tex]\[
\text{Total work required (in wall-days)} = 25 \text{ walls} \times \frac{25 \text{ days} \times 50 \text{ workers}}{50 \text{ walls}} = 625 \text{ wall-days}
\][/tex]
4. Calculate the number of days needed for 25 workers to complete 625 wall-days of work:
- We now use the work rate per worker per day and the number of workers available.
[tex]\[
\text{Days needed} = \frac{\text{Total work (in wall-days)}}{\text{Number of workers} \times \text{Rate per worker per day}}
\][/tex]
[tex]\[
= \frac{625 \text{ wall-days}}{25 \text{ workers} \times 0.04 \text{ walls per worker per day}} = \frac{625}{1} = 625 \text{ days}
\][/tex]
Therefore, it will take 25 workers 625 days to build 25 walls.
