To solve this problem, we can follow these steps:

1. Determine the total amount of water needed: The hot tub has a volume of 258 gallons.

2. Determine the rate at which the hose fills the hot tub: The hose fills the tub at a rate of 4.75 gallons per minute.

3. Find the total time in minutes: $\text{Time (in minutes)} = \frac{\text{Total amount of water}}{\text{Rate of flow}} = \frac{258 \, \text{gallons}}{4.75 \, \text{gallons per minute}}$

4. Convert minutes to hours: Since there are 60 minutes in an hour, the conversion will be: $\text{Time (in hours)} = \frac{\text{Time (in minutes)}}{60}$

Let’s calculate this now:

$\frac{258}{4.75} = 54.32 \, \text{minutes}$

Now convert to hours:

$\frac{54.32}{60} = 0.91 \, \text{hours}$

So, it will take approximately 0.91 hours to fill the hot tub.

Would you like any further details or clarifications on this?

Here are 5 related questions to explore:

1. How many seconds will it take to fill the hot tub?
2. What if the rate was reduced to 3 gallons per minute? How long would it take then?
3. How long would it take to fill two such hot tubs?
4. How many gallons will be filled in half an hour?
5. What is the rate in gallons per second?

Tip: Always ensure to convert units consistently when solving problems involving rates and time.