The answer is really simple. While driving, you conditionally move from under one falling raindrop to another. That is, the total amount of precipitation falling from above does not depend on the speed of your movement.
To understand this, imagine that raindrops are stationary in the air, and you and the earth are moving towards these drops. And since the volume of the parallelepiped is equal to the area of the base of the parallelepiped multiplied by its height, no matter how fast you move, the same number of raindrops per second falls on your head.
If you don't move, then all you get is rain falling on you from above, but if you start moving, you additionally collect side raindrops from the facade. Thus, at any given second, you will be the driest if you remain motionless. And the faster you run, the faster you will get wet.
But if you need to get from point A to point B, then standing is not an option. The total amount of moisture that you will collect on the way to point B does not depend on the speed at which you will go. For example, a snowplow will collect the same amount of snow on a certain stretch of road and this amount will not depend on the speed of this machine.
When you choose the tactics of "running in the rain", imagine the parallelepiped again. As you can see, regardless of the speed of movement, you will get the same amount of precipitation falling on you from above and regardless of the speed, on a given segment you will get the same amount of precipitation from the side. Thus, the total degree of wetting = the product of humidity per second for the time spent in the rain + humidity per meter multiplied by the distance traveled.
To stay minimally wet, moving in the rain from one point to another, you need to try to minimize the amount of water falling on top of you and run as fast as possible.
Run, Forrest! Run!
