Brad Plumer presented a fun math problem this morning. But instead of using it to discuss why math makes everything better, he insisted upon discussing policy. Environmental policy, in fact. Now I’m all for that. You can decide for yourself if the article is worth reading from its title, Want to Boost Fuel Economy? Stop Thinking About Miles Per Gallon. It is worth reading! But I will give you the important conclusion: small increases in the mpg of gas hogs are far more important than big increases in the mpg of tiny cars that already have decent fuel economy. In other words, if you are shopping for a hybrid, mpg doesn’t matter that much. But if you are shopping for an SUV, you should pay close attention to minor differences in competing model fuel ratings.
How do we know this? Mathematics! All is revealed in the following puzzle:
Let’s assume that x is the number of miles that Dylan and Sarah each drive in a year. (I’ve already lost you, haven’t I? Pay attention! This is not just interesting; it is fun.) That means that the gallons of gas they each use is given by x divided by the mpg they get. So originally, Dylan uses x/29 gallons of gas per year. With his new car, he uses x/50 gallons. Similarly, Sarah uses x/12 gallons and x/15 gallons. The amount of gas they each save is given by the amount of gas they use with the new car subtracted from the amount they used with the old car:
To figure out who saves more gas, we just divide these two equations. This causes the number of miles (x) to cancel out and we get:
So Sarah will always save 15% more gas than Dylan for her small 3 mpg increase (25%) compared to his large 21 mpg increase (72%). You probably already know why this is: Sarah starts by using a huge amount of gas. In Plumer’s example, he uses 1,000 miles for his x value and finds that while Dylan decreases his gas consumption from 34 to 20, Sarah reduces her consumption from 83 to 67. In other words, she has more gas usage to save. Or think of it this way: imagine you have a car that gets a million miles to the gallon. If you drive 1,000 miles, you would only use 0.001 gallons of fuel. Getting a car with better gas mileage can’t same you more than 0.001 gallons.
So remember this if you are buying an SUV. And if you’re buying an SUV, I certainly hope that you have a very good reason!