https://file.aiquickdraw.com/mathbot/file/1725484405213b8yhq9bh.jpg

The problem states:

"Jody has already hiked 1 kilometer. The trail is 12 kilometers long, and she can hike 2.5 kilometers per hour. Which function will help Jody figure out how many more hours, \( h \), she needs to hike?"

We need to find a function that models how long it will take Jody to complete the remaining distance of the trail.

### Analysis:
1. **Total Distance**: The trail is 12 kilometers long.
2. **Distance Already Hiked**: Jody has already hiked 1 kilometer.
3. **Remaining Distance**: The remaining distance Jody needs to hike is \( 12 - 1 = 11 \) kilometers.
4. **Hiking Speed**: Jody can hike at a rate of 2.5 kilometers per hour.

### Function:
The time \( h \) in hours that Jody needs to hike the remaining distance can be calculated by dividing the remaining distance by her hiking speed:

\[
h = \frac{\text{Remaining Distance}}{\text{Hiking Speed}} = \frac{11}{2.5}
\]

This is the equation that represents the time Jody needs to complete her hike. However, the options presented are likely in a different form, typically in the form \( h = \text{some expression} \).

### Evaluating the Options:
Let's evaluate the options given in the image:

1. **Option 1: \( h = 2.5h + 12 \)**  
   This option incorrectly adds the distance and speed, which doesn't make sense.
   
2. **Option 2: \( 12 = 2.5h + 4 \)**  
   This equation incorrectly relates the total distance to speed times hours, and the "+4" term is not explained.
   
3. **Option 3: \( h = 4 + \frac{11}{2.5} \)**  
   This equation includes an extraneous "+4" term and is not correct.
   
4. **Option 4: \( h = \frac{12 - 1}{2.5} \)**  
   This is the correct function. It simplifies to \( h = \frac{11}{2.5} \), which is the time needed to hike the remaining distance.

### Conclusion:
The correct function is the one presented in **Option 4**: \( h = \frac{12 - 1}{2.5} \).

Would you like more details or have any further questions?

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Here are some related questions:

1. What is the significance of isolating the variable \( h \) in the equation?
2. How would the function change if Jody hiked at a different speed?
3. What if the trail was longer or shorter? How would the function adjust?
4. How would the equation be different if Jody had hiked more or less than 1 kilometer?
5. Can you express the time function in a different mathematical form?

**Tip:** Always double-check the context of each term when setting up your equations to ensure that you are correctly representing the physical situation.

Jody has already hiked 1 kilometer. The trail is 12 kilometers long, and she can hike 2.5 kilometers per hour. Which function will help Jody figure out how many more hours, h, she needs to hike?

Discover how to calculate the time Jody needs to finish her hike using the distance, rate, time relationship. This problem involves finding the correct function to model the situation, applying key concepts of linear equations. Ideal for students in Grades 6-8.

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