October 13th, 2007

xkcd - Escher

I solved my commute

Taking advice from y'all and others, and using a TI-89 to shave off the labor of doing derivatives by hand, I solved my commute. The optimal speed for me to drive based upon gas mileage and time spent is 95mph. Since I also want to take into account safety and tickets, this means drive as fast as I feel is safe and won't get me ticketed, so my current trend of going 75ish seems good to me, and I should *not* try to slow down.

SolutionCollapse )

The trivial solution is that I can minimize the cost of my trip in terms of both dollars and time if (x=0) I live in my office, or I work from home. A little further exploration showed that v=95 is a local minimum (good) and v=180 is a local maximum (bad). Despite the fact that the faster I drive, the worse my gas mileage, the time savings dominates until I reach 95pmh. At that point the gas mileage is bad enough that it makes the cost worse and worse until I hit 180mph - if I drive faster than that I should start saving money again.

So I think I determined the real reason that some people drive 95 mph on the highway: they're mathematicians!

x-posted to my journal