AutoMathically Challenged

Which will save you more gas, upgrading from an SUV that gets 10 miles per gallon to a car that gets 20? Or, switching a 30 mpg compact for a hybrid that gets 60 mpg (more than the Prius gets, but lets just say, for the sake of argument)?

Both are a doubling of gas mileage, and the latter is an increase of a whopping 30 mpg, so surely the second is better, right? If you think so, you’re not alone, according to a paper published yesterday in Science. But you’re also wrong.

The researchers who published the study argue that people make better decisions about fuel savings when fuel economy is presented in gallons per mile instead of miles per gallon.

Here are some numbers from the example above:

10 mpg=10 gallons per 100 miles
20 mpg=5 gallons per 100 miles

30 mpg=3.33 gallons per 100 miles
60 mpg=1.67 gallons per 100 miles

So, the savings in the first case is 5 gallons per 100 miles or about $20, while the savings in the second case is 1.67 gallons per 100 miles or about $6.70. Clearly, upgrading from a really inefficient car to something even marginally more efficient makes more of a difference than improving on an already good option.

The reason for this perhaps counterintuitive result is that as a number increases linearly, its inverse does not show a linear decrease. Check out the graph above: it’s clearly not a straight line. It also highlights the authors’ point that the greatest gains in gallons saved come from changes at the lowest miles per gallon, so we really need to lop off the left part of the curve.

Why does such simple math deserve a Science paper? The authors showed that most people don’t get this relationship.

They asked one group of students which choice would save more gas: to replace a fleet of cars getting 15 mpg with vehicles getting 19 mpg, or to replace an equal number of cars getting 34 mpg with ones getting 44 mpg. Seventy-five percent of students picked the latter.

Another group was given the same choice but with the information also presented in gallons per mile. This time, 65 percent of students made the right choice: choosing to replace the first group of cars.

Maybe $4 a gallon gas (that’s 0.25 gallons per dollar, by the way) will at least be good for our math skills.

Comments

[Random Comment Generator]

Hi there, you know, I literally printed this out and brought it with me to the car dealership last weekend. I was considering the Honda Civic, Fit, and Element (which I love, but gets 1/3 fewer mpg). Calculating the old way, the difference didn't seem so extreme. Calculating your way, I could not deny that the difference between the Civic and the Fit was negligible but the Element is in a whole other category, one I can't justify being in no matter how many dogs can fit inside. So, from a math-challenged environmentalist, thanks for your help.

[Jessica Marshall]

RCG, Your comment makes me so happy to read. I expect this is exactly the sort of decision-making the authors were hoping to influence. And to make a difference just days after the paper was released! :)

I can't imagine my 1988(!) Honda Civic will last much longer, so I'll soon be in your car-comparing shoes. I'm glad for the new insight, too.