The number of hours required to build a fence is inversely proportional to the number of people working on the fence. If it takes 8 people, 40 hours to complete the fence, then how long will it take 17 people to build the fence? (round answer to 2 decimal places if needed)

 hours.

The number of hours required to build the fence is inversely proportional to the number of people working on it. This means:

\[
\text{Hours} \times \text{People} = \text{Constant}
\]

Given:
- 8 people take 40 hours, so:

\[
8 \times 40 = 320
\]

This means our constant is 320. Now, let \( x \) be the number of hours it will take 17 people to complete the fence:

\[
17 \times x = 320
\]

Solving for \( x \):

\[
x = \frac{320}{17} \approx 18.82
\]

So, it will take approximately **18.82 hours** for 17 people to build the fence.

Would you like more details or have any questions?

Here are five related questions to deepen understanding:
1. What if 10 people worked on the fence? How many hours would it take?
2. How would the total time change if each person worked at 90% efficiency?
3. What formula represents inverse proportionality in other scenarios?
4. What happens if the number of people doubles? How does the time adjust?
5. Can the inverse proportion method apply if the work rate per person varies?

**Tip:** In problems involving inverse proportionality, increasing one variable decreases the other proportionally.

The number of hours required to build a fence is inversely proportional to the number of people working on the fence. If it takes 8 people, 40 hours to complete the fence, then how long will it take 17 people to build the fence? (round answer to 2 decimal places if needed)

Discover how to solve an inverse proportion problem: If 8 people take 40 hours to build a fence, calculate the time needed for 17 people. This solution covers concepts like inverse proportionality and algebraic calculations, ideal for Grades 7-9.

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