During a comping trip. Aundria and Annette decide to travel to their campsite using two different routes. Aundria takes the hiking trail that travels 5 miles south, 6 miles east, 7 miles south, and 2 miles west to the campsite, Annette uses the cross-country route that starts at the same point as the kiking trail but goes in a straight line from there to the campsite. About how many miles total will the two travel?

Options

A. `32.65`
B. `33.42`
C. `34.00`
D. `34.42`

Answer

To solve the problem, we need to calculate the distances traveled by Aundria and Annette separately and then find the total distance they traveled together.

### Step-by-Step Solution:

1. **Calculate Aundria's Distance**:
- Aundria travels:
- 5 miles south
- 6 miles east
- 7 miles south
- 2 miles west
- Total distance traveled by Aundria:
\[ \text{Distance} = 5 + 6 + 7 + 2 = 20 \text{ miles} \]

2. **Visualize Annette's Route**:
- Annette travels in a straight line from the starting point to the campsite. To find this distance, we can visualize the path taken by Aundria as a right triangle.
- The vertical distance (south) is:
\[ 5 + 7 = 12 \text{ miles} \]
- The horizontal distance (east-west) is:
\[ 6 - 2 = 4 \text{ miles} \]

3. **Use the Pythagorean Theorem**:
- We can now use the Pythagorean theorem to find the straight-line distance (hypotenuse) that Annette travels:
\[ \text{Distance}^2 = \text{Vertical Distance}^2 + \text{Horizontal Distance}^2 \]
\[ \text{Distance}^2 = 12^2 + 4^2 \]
\[ \text{Distance}^2 = 144 + 16 = 160 \]
\[ \text{Distance} = \sqrt{160} \approx 12.65 \text{ miles} \]

4. **Calculate Total Distance**:
- Now, we add the distances traveled by Aundria and Annette:
\[ \text{Total Distance} = \text{Distance by Aundria} + \text{Distance by Annette} \]
\[ \text{Total Distance} = 20 + 12.65 = 32.65 \text{ miles} \]

### Final Answer:
The total distance traveled by Aundria and Annette is approximately **32.65 miles**.

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