https://file.aiquickdraw.com/mathbot/file/1726694957626z3ylety9.jpg

To find the shortest route from Greenwood to Middletown using the paths shown in the image, we need to evaluate all possible routes:

1. **Direct route from Greenwood to Middletown**:
   - Greenwood → Allenville (9.7 miles) + Allenville → Middletown (13.7 miles) = **23.4 miles**.

2. **Route via Rockport**:
   - Greenwood → Rockport (21.9 miles) + Rockport → Middletown (10.2 miles) = **32.1 miles**.

3. **Route via Lowell** (not directly relevant for shortest path):
   - Greenwood → Rockport (21.9 miles) + Rockport → Lowell (13.6 miles) = **35.5 miles**, but there's no connection from Lowell to Middletown shown.

The **shortest route** is **23.4 miles** through Allenville.

Would you like more details on how the distances were calculated or any additional information? Here are some related questions:

1. How can you verify the shortest path using a different method?
2. What if we had more towns connected—how would this affect the shortest path?
3. How does Dijkstra's algorithm work for finding the shortest path in graphs like this one?
4. What tools can be used to solve real-world shortest path problems?
5. Could geometry (e.g., angles) play a role in optimizing the route further?

**Tip**: When solving shortest path problems, organizing the paths in a list or table can make comparisons clearer.

Using the paths shown, how long is the shortest route from Greenwood to Middletown?

Determine the shortest route from Greenwood to Middletown using the distances provided in the diagram. Compare paths through Allenville and Rockport to find the shortest path. This problem introduces basic graph theory and distance addition, suitable for Grades 6-8.

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