Bigger Impact: 15 to 18 mpg or 50 to 100 mpg?

Posted on December 23, 2007  Comments (9)

This is a pretty counter-intuitive statement, I believe:

You save more fuel switching from a 15 to 18 mpg car than switching from a 50 to 100 mpg car.

But some simple math shows it is true. If you drive 10,000 miles you would use: 667 gallons, 556 gallons, 200 gallons and 100 gallons. Amazing. I must admit, when I first read the quote I thought that it must be an wrong. But there is the math. You save 111 gallons improving from 15 mpg to 18 mpg and just 100 improving from 50 to 100 mpg. Other than those of you who automatically guess that whatever seems wrong must be the answer when you see a title like this I can’t believe anyone thinks 15 to 18 mpg is the change that has the bigger impact. It is great how a little understanding of math can help you see the errors in your initial beliefs. Via: 18 Is Enough.

It also illustrates that the way the data is presented makes a difference. You can also view 100 mpg as 1/100 gallon per mile, 2/100 gallons per mile, 5.6/100 gpm and 6.7 gpm. That way most everyone sees that the 6.7 to 5.6 gpm saves more fuel than 2 to 1 gpm does. Mathematics and scientific thinking are great – if you are willing to think you can learn to better understand the world we live in every day.

Related: Statistics Don’t Lie, But People Can be FooledUnderstanding DataSeeing Patterns Where None ExistsOptical Illusions and Other Illusions1=2: A Proof

9 Responses to “Bigger Impact: 15 to 18 mpg or 50 to 100 mpg?”

  1. turtie
    December 25th, 2007 @ 4:59 am

    Nice site here!! The challenge question can be quite difficult! Some nice information and facts; I subscribed. (Yes, I’m an engineer!)

  2. No name provided
    March 17th, 2008 @ 9:31 pm

    So what you are saying is if I drive a car that gets
    15mpg I’ll have to pay for 667 gallons
    18mpg I’ll have to pay for 556 gallons
    50mpg I’ll have to pay for 200 gallons
    100mpg I’ll only have to pay for 100 gallons

    Wow, your right I’ll keep driving my 100mpg Plug-in Hybrid until I can get my hands on an all electric car.

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    May 12th, 2008 @ 10:21 am

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  4. Ewan Kennedy
    August 14th, 2008 @ 9:13 am

    It seems almost like an illusion or trick when you first read it. I actually took the reciprocals and proved it to myself before reading the second paragraph. But had I not already been alerted to the fact that this was a paradox, I probably would have given the wrong answer. The other way of looking at it, for those who don’t like fractions or algebra, is to say this. It is clear that, by switching from the 50 mpg car to the 100 mpg car, one gets far more miles to the gallon than if one were to have made the other choice (50 more versus 3 more). And if that option gives you far more miles to the gallon, then it must give you less gallons to the mile. It’s the gallons that you have to pay for and which therefore drive the savings.

  5. Hendrik
    October 18th, 2008 @ 11:40 am

    This is very much interesting it’s like a trick but it is fact !!! And if that option gives you far more miles to the gallon, then it must give you less gallons to the mile. It’s the gallons that you have to pay for and which therefore drive the savings.

  6. Dell
    December 5th, 2008 @ 11:45 am

    I like the trick and it would be a very good marketing (manipulation) tool. However, the fact remains that even though I am saving 111 gallon from 15 to 18 mpg, I am still using more fuel. I know everyone has seen this and we are all quite smart to figure out the math manipulation. However, I would venture to guess that the majority of Americans could care less about the bigger picture. With gas prices falling down below $2/gallon, how many people will really care what gas mileage the vehicles get any more. Bring on the SUV’s, GM doesn’t need a bailout anymore.

    I truly would like to see gas prices spike up again before we forget about alternative fuels.

  7. Patrick
    December 12th, 2008 @ 7:34 am

    I’ve seen this before, and at first glance it seems counterintuitive, but when you examine the math for a few moments it is clear. Unfortunately, I don’t think Congress and the car companies are focusing too much on the big rigs, semis, and other commercial transports that get less mileage than this example, but drive a large portion of our nations miles. I’m still in favor of increasing efficiency at all levels.

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