Re: When it is raining outside, will I get wetter if I run fast or walk slow?

To answer a question like this, we normally use a mathematical model.
There is not really anything very special in the science -- it is more a
matter of thinking your way through the math. I hope you will be able 
to follow the way I have done it.

We start with some simplifying assumptions. We assume there is no 
wind, and that therefore the rain falls vertically. We also assume that 
you are box shaped, with height that we will call "height", front to back
width that we will call "width", and shoulder to shoulder width that does
not matter because it doesn't affect anything.

Here is a picture of what is going on.



If the forward speed of the runner is V(run), and the speed of fall of the 
raindrops is V(fall), then in 1 second, all of the rain in the funny shaped 
volume shown on the left of the diagram will hit the runner.

The right hand side of the diagram shows how to rearrange that volume 
into a rectangle (really a box, if you think of the shoulder to shoulder 
width as the third dimension). The width of the rectangle is "V(run)". The 
height of the rectangle is height, plus a little bit extra shown by the small 
blue vertical line near the top of the right hand diagram.

We can calculate the height of this small blue vertical line as

"width" * "V(fall)" / "V(run)"

So in 1 second, you will be hit by all the rain in a volume

"V(run)" * ["height" + "width" * "V(fall)" / "V(run)"] * "shoulder to shoulder".


The number of seconds it will take you to reach shelter is given by

"distance" / "V(run)".

So the amount of rain that will hit you on the way to shelter is

"V(run)" * ["height" + "width" * "V(fall)" / "V(run)"] * "shoulder to shoulder".

The only place that the speed you run at will make a difference is in that very
small term represented by the vertical blue line. The faster you run, the better,
but only by a very tiny amount.

There are two other things I should say: 
first, if there is any wind, the whole analysis changes a little, but the general 
conclusion is the same, and you are much better off to run downwind towards 
shelter than into the wind, which I am sure you knew anyway.
second, in terms of your general personal comfort, the best thing to do (if you
can do it safely) is to walk rapidly backwards towards the shelter!