The problem states:

• 20 builders working 6 hours a day can finish a building in 30 days.
• We need to find out how many builders would be required to finish the building in 20 days if they worked for 10 hours a day.

Solution:

First, let's calculate the total amount of work done in builder-hours under the given scenario:

1. Total work done (builder-hours) in the original case:
   • 20 builders × 6 hours/day × 30 days = 3600 builder-hours.

Now, we need to determine how many builders are required to finish the same amount of work in 20 days if they work 10 hours a day:

2. Total work needed in new scenario:
   • Let the number of builders required be $x$.
   • The total work they will do in 20 days at 10 hours/day is $x \times 10 \times 20$.

We want this to equal the total work from the original case: $x \times 10 \times 20 = 3600$

3. Solving for $x$: $x \times 200 = 3600$ $x = \frac{3600}{200} = 18$

Thus, 18 builders would be required to finish the building in 20 days if they work 10 hours a day.

Do you have any questions or would you like further details? Here are 5 related questions for further exploration:

1. If the number of days were reduced to 15, how many builders would be needed if they still worked 10 hours a day?
2. What if the builders worked 8 hours a day instead of 10, how many builders would be required?
3. How would the calculation change if the productivity of each builder varied?
4. If 25 builders were available, how many days would it take them to finish the building working 10 hours per day?
5. What if the total hours of work required increased by 20% due to unexpected changes in the project?

Tip: When solving work-related problems, always remember to compute the total amount of work done (e.g., worker-hours) and then adjust based on the variables that change (time, number of workers, or hours worked per day).