# Walking or Running in The Rain

I al­ways am amazed by peo­ple sug­gest­ing that walk­ing in the rain keeps you dry­er than run­ning. Just saw an an­swer to this. Check it out, it's nice:

I have al­so seen it de­bunked ex­per­i­men­tal­ly, by Myth­Buster­s. But let's try a dif­fer­ent ap­proach: in­tu­itive math. In­tu­itive math is tricky be­cause it usu­al­ly is wrong, but hey, it's fun.

Ap­par­ent­ly, we all agree that how wet you get cor­re­lates to your speed. Oth­er­wise, the ques­tion is point­less be­cause the an­swer is "walk or run, but take an um­brel­la", while true, is cheat­ing, right?

So, for those slow­er-is-­bet­ter pro­po­nents: go and walk very, very, very slow­ly. You may no­tice that you end com­plete­ly soaked be­fore you fin­ish walk­ing. If you did­n't, you are still walk­ing too fast.

On the oth­er hand, if you were to go at 1000000 km/h we all agree you would on­ly get some drops in your frontside, right? Which would not soak you. Right? And most im­por­tant­ly, is con­stant re­gard­less of your speed, be­cause it's just the av­er­age amount of wa­ter con­tained in a man-shaped prism from point A to point B, and you get that wa­ter in your front if you go slow any­way.

As­sum­ing the speed/­soak­i­ness curve is rough­ly monotonous, it's clear that the max­i­mum soak­i­ness is when you go slow­est.

If it's not monotonous, then the ques­tion is rough­ly unan­swer­able, since it would in­volve there is an op­ti­mal speed and it's worse to go ei­ther faster or slow­er than that, which means the an­swer is some­thing like "jog" which is not what you wan­t.

So, go fast, go dry.

/ 2012-12-24 03:05:

Another way to think it is backwards. Let's say that "no matter how fast you're going, you'll receive the same amount of water".

So, if you walk/run at X km/h you get some water. If you walk/run at X/2 km/h, you get same amount of water. Same for X/4, X/8, etc. Let's call your speed S, and W the amount of water.

We're saying that with S getting smaller, W stays steady. What if S is zero? That means that you're not advancing, so you will get *a lot* of water, and that contradicts the hypothesis.

You can say "wait! zero is a special case!". Well... that would mean that W stays steady with S getting really really really small, and for 0 it will jump to infinite. That would imply a discontinuity, and nature doesn't like that.

So, conclusion: W goes up if S goes down. In other words, go fast, go dry ;)