The author takes several factors into account and models the total amount of water a person absorbs as
This assumes a person is essentially a rectangular box of height l, width w, and thickness t. The rain is falling at an angle θ to the vertical (e.g. θ = 0 for rain coming straight down). The distance you need to walk or run is d and your speed is v. The rain is falling with speed c. The parameter I is the rain intensity, ranging from 0 for no rain to 1 for continuous flow. The book goes into greater detail, deriving the formula and estimating numerical values for the parameters.
If the rain is driving into you from the front, run as fast as you safely can. On the other hand, if the rain is coming from behind you, and you can keep pace with its horizontal speed by waling, do so!