Step 1: Understanding solvolysis.
Solvolysis of alkyl halides proceeds via formation of a carbocation intermediate. The more stable the carbocation, the faster the solvolysis rate. Aromatic and benzylic systems show enhanced carbocation stability due to resonance. Step 2: Comparing structures.
Structure III forms the most stable carbocation because the benzylic position allows extensive resonance stabilization. Structure II forms an allylic carbocation, which is moderately stabilized. Structure I forms the least stable carbocation because the vinyl halide does not form a stable carbocation and no resonance stabilization is possible. Step 3: Conclusion.
Thus the rate of solvolysis follows: III>II>I.