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The problem states that the time it takes Noah to fill the pool is inversely proportional to the number of hoses he uses. When he uses 6 hoses, it takes 36.5 seconds. The goal is to find how long it will take using 5 hoses.

In problems of inverse proportion, the formula used is:

\[
T_1 \times H_1 = T_2 \times H_2
\]

Where:
- \(T_1 = 36.5 \) seconds (time with 6 hoses),
- \(H_1 = 6 \) hoses,
- \(T_2 = ?\) seconds (time with 5 hoses),
- \(H_2 = 5 \) hoses.

We can rearrange the equation to solve for \(T_2\):

\[
T_2 = \frac{T_1 \times H_1}{H_2}
\]

Substituting the known values:

\[
T_2 = \frac{36.5 \times 6}{5}
\]

Now, let's calculate this.The time it will take Noah to fill the paddling pool using 5 hoses is **43.8 seconds**.

Would you like further details or have any questions?

Here are some related questions:
1. How does the formula change if the relationship is directly proportional?
2. What would happen to the time if Noah used 4 hoses instead of 5?
3. How long would it take to fill the pool with 3 hoses?
4. What if Noah used only 1 hose? How long would it take?
5. What if the time with 7 hoses was given instead—how would you solve for 6 hoses?

**Tip:** In inverse proportionality, as one quantity increases, the other decreases, maintaining a constant product.

Noah is filling a paddling pool with water. The time that it takes him to fill the pool is inversely proportional to the number of hoses that he uses. When he uses 6 hoses, it takes 36.5 seconds to fill the pool. How long, in seconds, will it take Noah to fill the paddling pool using 5 hoses?

Learn how to solve a problem involving inverse proportionality. In this example, Noah fills a pool using 6 hoses, which takes 36.5 seconds. Calculate how long it will take with 5 hoses using algebraic methods. Suitable for Grades 6-8.

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