**AMBULANCE** 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? Round your answer to the nearest tenth, if necessary.



To determine where the ambulance should park between the Davis Medical Center and Woodland Hospital, we'll again use the concept of weighted averages. 

### Let's define the problem:

- Let \( D \) represent the location of Davis Medical Center.
- Let \( W \) represent the location of Woodland Hospital.
- The weight of Davis Medical Center is \( 4w \).
- The weight of Woodland Hospital is \( w \).

### Weighted Average Formula:
The formula to find the weighted average location \( P \) for the ambulance is:
\[
P = \frac{( \text{Weight of Davis} \times D ) + ( \text{Weight of Woodland} \times W )}{\text{Total Weight}}
\]

Substituting the given weights:
\[
P = \frac{(4w \times D) + (w \times W)}{4w + w}
\]
\[
P = \frac{4w \times D + w \times W}{5w}
\]
\[
P = \frac{4D + W}{5}
\]

### Conclusion:
- The ambulance should park at a location that is \( \frac{4}{5} \) (or 80%) of the distance from Woodland Hospital toward Davis Medical Center.

Without specific locations for \( D \) and \( W \), the formula tells us that the ambulance should be positioned closer to Davis Medical Center, precisely 80% of the way from Woodland Hospital to Davis Medical Center.

### Example (Rounded to the Nearest Tenth):
- If \( D \) is at 0 miles and \( W \) is at 10 miles:
\[
P = \frac{4(0) + 10}{5} = \frac{10}{5} = 2 \text{ miles from Davis Medical Center}
\]
So, the ambulance should park 2 miles from Davis Medical Center or 8 miles from Woodland Hospital.

Would you like more examples or have any other questions?

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**Related Questions:**
1. How would the answer change if Davis Medical Center's weight was only 3 times that of Woodland Hospital?
2. What if the distance between the two hospitals was different, say 15 miles?
3. How does this method apply to three or more hospitals?
4. Can the weighted average method be applied if hospitals have different operating hours?
5. How would geographical obstacles (like rivers) between the hospitals affect the parking decision?

**Tip:** Always verify the sum of weights when calculating weighted averages to ensure accurate results.

Learn how to determine where an ambulance should park between Davis Medical Center and Woodland Hospital using weighted averages. Understand the application of weighted average formulas in practical scenarios. Example calculations provided.

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