Explanation:

Let’s break it down step by step:

- The directions mean:

@ is east, * is west, # is south, & is north.

- V’s full path:

A *16 B #10 C @8 D #14 E *23 F &16 W

- A is the starting point.

- *16 B: B is 16 km west of A.

- #10 C: C is 10 km south of B.

- @8 D: D is 8 km east of C.

- #14 E: E is 14 km south of D.

- *23 F: F is 23 km west of E.

- &16 W: W is 16 km north of F.

- What matters for B and W is their coordinates relative to A.

- Start at A (0,0).

- B: (-16,0)

- From B, go south 10: (-16,-10) for C

- From C, east 8: (-8,-10) for D

- From D, south 14: (-8,-24) for E

- From E, west 23: (-31,-24) for F

- From F, north 16: (-31,-8) for W

- Now, B is at (-16,0), W is at (-31,-8).

- Use the distance formula:

v[(x2-x1)² + (y2-y1)²]

= v[(-31+16)² + (-8-0)²]

= v[(-15)² + (-8)²]

= v[225 + 64]

= v289

= 17 km

So here’s the thing:

- Option 3 (17 km) lines up exactly with the math above.

- The other options don’t match our calculation.

- Option 3: 17 km is the correct answer.