This problem can be solved using the concept of work-rate.

Given:

• 24 builders can build the wall in 96 days.
• We need to find out how long it would take for 36 builders to build the same wall.

Step 1: Determine the total amount of work (in builder-days).

The total work required to build the wall is the product of the number of builders and the number of days: $\text{Total work} = 24 \, \text{builders} \times 96 \, \text{days} = 2304 \, \text{builder-days}$

Step 2: Calculate the time for 36 builders to complete the same work.

If 36 builders are working, the number of days required to complete the work $T$ can be found by dividing the total work by the number of builders: $T = \frac{\text{Total work}}{\text{Number of builders}} = \frac{2304 \, \text{builder-days}}{36 \, \text{builders}} = 64 \, \text{days}$

Conclusion:

It would take 36 builders 64 days to build the same wall.

Would you like more details, or do you have any questions?

Here are 5 related questions to consider:

1. How would the time change if the number of builders doubled?
2. What if the builders worked fewer hours each day?
3. How long would it take if only 12 builders were working?
4. Can you generalize a formula for the time required based on any number of builders?
5. How does this scenario change if the builders are not equally efficient?

Tip: When solving problems involving rates of work, always check if the problem assumes constant efficiency or if there are variables like fatigue or varying hours that might affect the calculations.