Do you find this counter-intuitive?

Beth. ? Unless there is something in the problem they aren’t telling us.

Key point: city driving or freeway driving. Freeway driving is considerably more fuel efficient than city driving.

Other factors:

- is the air conditioning on in either car?
– who does more uphill driving?

Adam’s savings is the difference between 0.0833 gallons per mile and 0.0714 gallons per mile, times the number of miles driven. Let’s say 1000 miles to make a simple example:
(0.0833 – 0.0714) * 1000 = ~12 gallons

Beth’s savings aren’t so dramatic. Her original gallons per mile figure was 0.0333, and her improved mileage rate is 0.025, multiply that difference by the same 1000 miles to arrive at a savings of around 8.3 gallons.

Looks like Adam saves more.
If both drivers drive their cars 120 miles, Adam saves enough gas to go another 20 miles or a little more than 1⅓rd gallons of gas.
Beth only saves enough gas to go another 40 miles, or 1 gallon.

12 mpg; 14 mpg
= 1/12 gallon per mile; 1/14 gallon per mile
= 14/168 gallon per mile; 12/168 gallon per mile

Savings: 1/84 gallon per mile

30 mpg; 40 mpg
1/ 30 gallon per mile; 1/ 40 gallon per mile

40/1200 gallon per mile; 30/1200 gallon per mile

Savings: 1/120 gallon per mile

Adam saves 1/84 gallons per mile when we compare his new car to his old car; Beth saves 1/120 gallon per mile when we compare her new car to her old car.

Based on that comparison, Adam saves more gas… At least, I think that’s how the calculations are supposed to go?

But it feels like a bit of an artificial comparison. Looking at each car’s mileage as a whole, Betty’s gas savings blow Adam’s out of the water, which is where I want to go intuitively. Adam’s still driving a gas guzzler. He’s still eating up more gas than she is per mile.

I’ve never found any counters intuitive. Flat and useful but rather dense.

This is an example of how “facts” and “numbers (statistics) distort the truth.

The “counter-intuitiveness” lies in how much more is one saving over another.

Beth doesn’t spend spend as much as Adam before or after.

Using CWOTUS’s 1,000 miles per year each, 500 before the change, 500 after. At $3 gallon,

Adam uses 41.67 gallons the first half, 35.71 the second half, or 125.01 +$107.14 =$232.15
Adam “saves” $17.87
Beth uses 16.67 gallons the first half, 12.5 gallons the second half, or $50.00 + $37.50 = $87.50 total.
Beth only “saves” $12.50.

Beth saves a helluva lot more overall than Adam.

I thought Adam saved more and my thinking was the same as @Soubresaut

Let’s simplify it. They both put 1 gallon of gas in their car. They drive from the same point A to the same point B on the same road at the same speed. Point B is 40 miles from point A.
Beth drives 40 miles and runs out of gas.
Adam drives the same distance, but he has to stop and put one gallon of gas in his car almost 3 times along the way before he gets there. (2.86 times.)

Is there something wrong with that logic?

@zenvelo , Suppose the statement of the problem was modified as follows. There is just one person, who owns a 30 mpg car and a 12 mpg truck. Each one gets driven the same distance. Which would save more fuel, replacing the car with a 40 mpg car or replacing the truck with a 14 mpg truck?

How about if everyone joins the world at large – abandon gallons and measure in litres?

This question was posted to Social, so meandering is permitted…nay, encouraged.

Road trip? We all have to pitch in for gas, you know.

@Love_my_doggie The person who got the 40 mpg car would save more.

It also depends on how Beth looks at her results, and Adam looks at his.

Can you give us an example @kritiper?

Beth saves enough to go 40 more miles.
Adam saves enough to go 20 more miles.
To Adam, that might be a good result of his purchase. Beth might feel the same.
The two individuals and their respective cars and/or results ARE NOT RELATED.

Here is a way that intuition might be used to look at this problem. If you want to save fuel costs, look at the largest offender, which would be the 12 mpg car.

I guess I don’t understand why this isn’t simply obvious.

Most people think that, since 40/30 is larger than 14/12, that switching from 30 mpg to 40 mpg will save more in fuel costs. What you should do is think in terms of gallons per mile. Now we have 30/40 is less than 12/14.

One car goes from 12 miles to the gallon to 14 miles to the gallon.

The other goes from 30 miles to the gallon to 40 miles to the gallon.

The first car get 2 miles to the gallon more.

The second car gets 10 miles to the gallon more.

It is not mpg that matters but gallons per mile, as I will show.

I am going to use // for division instead of / because the text is formatted oddly for /, like this ½0.

Beth’s car goes from 1//30 gallons per mile to 1//40 gallons per mile for a decrease of .008333 gallons per mile. Adam goes from 1//14 gallons per mile to 1//12 gallons per mile for a decrease of .0119 gallons per mile. If both cars travel 10,000 miles, Adam will use 119 fewer gallons and Beth will use 83 fewer gallons.

You can also do this as 10000//30 – 10000//40 = 333 – 250 = 83 gallons compared to
10000//12 – 10000//14 = 833 – 714 = 119 gallons.

Does Beth care about Adams mpg or gpm?
Does Adam care about Beth’s mpg or gpm?
Looks like the only person or persons who might care are the people who sold them the gas.

Jesus Christ, I’m gettin’ a headache….

Is this Beth at all good-lookin’ ??

No she ugly. Adam is a hunk though.