Flaneur in the rain - iv

Suppose you're sauntering about Saint-Germain, Paris, from one cafe to the next, staying only as long as it takes you to knock down a few Brilliant problems. You're wrapping up at Brasserie Lipp and want to go to Cafè de Flore, which is 80 m\text{80 m} away.

The only problem is: it's pouring rain!

Suppose now that your hat and your coat absorb water with different efficiencies ϵhead\epsilon_\text{head}, and ϵbody\epsilon_\text{body}. How should you change your running speed in order to absorb as little water as possible?

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