To solve this problem, we can use the concept of work rate. The work done is directly proportional to the number of builders and the number of days worked.

Here’s how we can break it down:

• 9 builders complete the job in 12 days.
• The total amount of work done is represented by 9 builders × 12 days = 108 builder-days.

Now, we want to find out how many days (x) it will take for 6 builders to complete the same amount of work:

• The equation becomes:
  6 builders × x days = 108 builder-days

To find x (the number of days), we divide the total work by the number of builders:

$x = \frac{108}{6} = 18 \text{ days}$

So, it will take 6 builders 18 days to complete the same job.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. What happens if you increase the number of builders to 12? How many days will it take?
2. If 4 builders were to work on this job, how many days would they need?
3. How do we calculate the work rate of a single builder in this scenario?
4. What if the 9 builders took 10 days instead of 12? How would that change the result?
5. If 6 builders worked for 9 days, how much of the job would they complete?

Tip: Always check if the number of workers or time is directly proportional when solving these types of problems.