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To solve this problem, we need to use the concept of a weighted average based on the weights of the two hospitals.

### Given:
- The map shows two hospitals: **Woodland Hospital** (at mile marker 24) and **Davis Medical Center** (at mile marker 31).
- **Davis Medical Center** has a weight that is 4 times that of **Woodland Hospital**.
  
Let the weight of **Woodland Hospital** be \( w_1 \) and the weight of **Davis Medical Center** be \( w_2 \). According to the problem:

\[
w_2 = 4w_1
\]

The location of the ambulance should be based on the weighted average of the hospital locations. The formula for the weighted average is:

\[
\text{Weighted Average} = \frac{(x_1 \times w_1) + (x_2 \times w_2)}{w_1 + w_2}
\]

Where:
- \( x_1 = 24 \) (location of Woodland Hospital)
- \( x_2 = 31 \) (location of Davis Medical Center)
- \( w_2 = 4w_1 \)

Now let's calculate this.

### Step 1: Set up the formula

Substitute the values into the weighted average formula:

\[
\text{Weighted Average} = \frac{(24 \times w_1) + (31 \times 4w_1)}{w_1 + 4w_1}
\]

### Step 2: Simplify the equation

\[
\text{Weighted Average} = \frac{24w_1 + 124w_1}{5w_1}
\]

\[
\text{Weighted Average} = \frac{148w_1}{5w_1}
\]

Since \( w_1 \) cancels out:

\[
\text{Weighted Average} = \frac{148}{5} = 29.6
\]

### Final Answer:

The ambulance should park at **mile marker 29.6**.

Would you like a detailed breakdown of the concept or have any other questions?

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Here are 5 related questions:
1. How would the parking position change if Davis Medical Center had double the weight of Woodland Hospital instead of 4 times?
2. Can you calculate the ambulance's parking position if Woodland Hospital was at mile marker 20 instead of 24?
3. What happens to the weighted average if both hospitals have the same weight?
4. How can the concept of weighted averages be applied to real-life decision-making scenarios outside of ambulance placement?
5. How would adding a third hospital between these two affect the placement of the ambulance?

**Tip**: Weighted averages are not just useful in positioning, but also in statistics, finance, and other fields where different items have varying levels of importance.

Some ambulances use weighted averages to find where to park between cities. The weight of a hospital is determined by the average number of emergent patients that need to be taken to the hospital on a daily basis. The Davis Medical Center usually has a weight 4 times that of Woodland Hospital. Where should the ambulance park?

Learn how to calculate the optimal parking position for an ambulance between Woodland Hospital and Davis Medical Center using weighted averages. This problem covers key algebraic concepts and is suitable for students in Grades 8-10. The solution involves understanding the concept of weighted averages, using the formula to determine that the ambulance should park at mile marker 29.6.

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