How Fast to Drive

I suppose this is sort of a commentary on the way my mind works – just the fact that I’ve actually spent time thinking about this. I’m not actually talking about some moral idea about what is the right or wrong speed to drive. I’m trying to argue that there is, in fact, a best speed to drive (relative to the conditions on that particular road at that particular time). Here there are several factors that make this work. I’m going to use money as a scale on which to rate all these things. After all, time is in some sense equivalent to money. Driving faster has advantages and disadvantages. Let’s look at it from the perspective of driving faster.

Driving faster gains you money. While you use slightly more gas and thus more money, you save yourself time by driving faster, and to a point this increases the total amount of money you have. By getting someplace sooner, you have more time to do whatever it was you want to be doing there. Thus, overall, you increase your free time, which is worth money. Besides this, driving more slowly than traffic increases your odds of being in an accident (people have to be constantly passing you and changing lanes, which increases their chances to do something dumb). This, of course, costs you lots of money. So, you might say, why not drive really fast then? Well, at some point, you clearly start incurring losses. Firstly, you will get more tickets, which cost you money. Secondly, you will exponentially increase your odds of getting in an accident, since you will be constantly weaving around other cars and thus increasing your opportunities to screw up. Finally, you will make any accidents you do get into even more severe, and increase your odds of dying in the accident – a scenario which has infinite cost to you.

Clearly, as you drive faster from 0 MPH, your money increases, thus the slope of our hypothetical money vs. speed curve here is positive. At the limit of driving really fast, your money decreases as you increase your speed, thus the slope is negative here. So, the slope of the money vs. speed curve is positive near 0, and negative near your maximum speed. The intermediate value theorem tells us that it must be 0 at some point in between (yay for math). This means that there is a speed which maximizes money (for you pedantic readers, yes, there could theoretically be more than one maximum, but I’m just arguing that there is at least one for now).

Personally, I believe that this best speed (or a best speed if more than one exists) is somewhere around 10 MPH greater than the posted speed limit. It may be somewhat less if you drive a car which will frequently get ticketed driving this speed, or while driving in a place known to be frequented by policemen. As I said before, this theoretical best speed is constantly changing based on the conditions at that point in time, but the fact that there is a “best” speed does not change.