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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.

Facundo Batista / 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 ;)

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