This problem involves the concept of work and the relationship between the number of workers and the time taken to complete a task. The more people working on the task, the less time it will take to complete, assuming all workers are equally efficient.

We can use the formula for inverse variation where $W$ is the amount of work (which is constant), $P$ is the number of people, and $T$ is the time:

$P_1 \times T_1 = P_2 \times T_2$

Given:

• $P_1 = 4$ people
• $T_1 = 55$ minutes
• $P_2 = 17$ people
• $T_2 = ?$ (we need to find this)

Using the formula:

$4 \times 55 = 17 \times T_2$

$220 = 17 \times T_2$

Solving for $T_2$:

$T_2 = \frac{220}{17}$

$T_2 \approx 12.94$

So, it would take approximately $12.94$ minutes for 17 people to build the fence.

Would you like more details or have any questions about the solution? Here are 5 questions you might consider asking next:

1. How does the formula for work apply to different types of tasks?
2. Can you provide more examples of inverse variation in real-life scenarios?
3. What assumptions are made in this type of problem regarding worker efficiency?
4. How would the time change if the efficiency of workers varied?
5. Can you explain the difference between direct and inverse proportionality in more detail?

Tip: When solving problems involving work and the number of workers, remember that the relationship is typically inversely proportional: as the number of workers increases, the time required to complete the task decreases.