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From a maths major: you'll end up drier running. Yeah, you'll sweep out the same area as you move, but a smaller amount of rain will have been present in that area while you were moving. Quite frankly, the idea that you'll be drier walking is stupid. Try it; walk slowly through the rain, and have a friend sprint through the rain. Your friend will be drier, every time. The discreet maths problem usually conveniently neglects the fact that the rain is moving, so you get bad results.
And if you're worried about splashes, dodge the puddles!
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Strewth
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