## 18 July 2008

### Five miles an hour = 30 cents a gallon?

"Every five miles an hour faster costs you an extra 30 cents a gallon." From yesterday's New York Times, among others. This is often mentioned in reference to bringing back the national 55 mile per hour speed limit.

What does this even mean? I assume it means that it takes, say, seven percent more gasoline per mile to drive 65 mph than to drive 60 mph. (30 cents is around seven percent of the current average gasoline price, \$4.10 or so per gallon.) Why not just say that? This also has the advantage that when gas prices change, the fact doesn't become outdated.

Although as many people point out, the lower speed limit is a hard sell, in part because of the value of time. If you're about to drive 65 miles at 65 mph, it'll take you an hour; say you get 20 miles per gallon, so that uses 3.25 gallons of gasoline. Slowing to 60 mph, it takes five minutes longer, but saves seven percent of that gasoline, or 0.23 gallons -- perhaps \$1 worth. So if you value an hour at more than \$12 (more generally, at more than three gallons of gasoline), you should drive faster! Of course I've committed the twin fallacies of "everything is linear" and a bunch of sloppy arithmetic, and I've ignored that different cars get different gas mileage, but the order of magnitude is right -- and it's clear to me some people value their time at more than this and some at less. And a better analysis would take into account the probability of getting in accidents, speeding tickets, etc. (I'm mostly pointing this out because otherwise some of you will.)

Oh, and on a related note, people will do things for \$100 worth of gas that they wouldn't do for \$100 worth of money.

Joey said...

Maybe I'm just dense first thing in the morning, but how can the price increase by seven percent per gallon? Shouldn't that be 7% per mile?

Also, you said "if you value an hour at...more than three dollars of gasoline", which I'm pretty sure should be "three gallons".

Michael Lugo said...

r,

thanks for catching that second error.

But the first one isn't an error at all. People are actually saying that the price increases by a certain amount per gallon.

Anonymous said...

I've always wondered about that statement as well. I assume the idea is to calculate the cost to drive a hundred miles at 55mph, then the cost of a hundred miles at 60mph and so on, then divide by the number of gallons it took you to drive at 55. It's more likely this is a number that someone made up a few years ago and people have been repeating ever since.

Anonymous said...

Lemma: the speed of light = 670,616,629 miles per hour.
Proof: convert from whatever units you prefer.

Divide this by 5 miles per hour and get this constant:

134,123,326

Dividing that by 30 cents per gallon and get:
4,470,777.53 gallons per cents and ...
what the heck was I doing?

Oh yeah, trying to figure out what it costs to go Warp 1 if no dilithium crystals are available, and the New York Times is to be believed.