# Question: can you properly explain a problem concerning ratios and such?

Question by : can you properly explain a problem concerning ratios and such?

http://www.sciencedaily.com/releases/2008/06/080619142118.htm

Is an article on why MPG should be changed to gallons per miles driven.

Not a bad idea, although everyone who totes it around as gallons per mile completely ruins any perceived benefit (my car gets .034 gallons per mile!)

anyway, my problem. The article points out how the majority of people believe that going from 34 MPG to 50 MPG saves more fuel than 18 MPG to 28 MPG, when this is in fact not the case.

driving 10 or 100 miles will show you that you save twice as many gallons switching from 18 to 28.

Numerically I get it and can see it, but not conceptually. So if in some more abstract way, can you explain WHY?
I am positive it has something to do with the fact that 34 and 50 are larger numbers therefore the larger difference (16>10) is of less importance. But that doesn’t explain it all really. What am I missing?

10 mpg over 10,000 miles- 1000 gal.
50 mpg over 10,000 miles- 200 gal

so its not that the fuel effieciecy is different, numerically its all even ofcourse. But why with the lower numbers, is the savings larger? it has something to do with ratios right>>>???

Best answer:

Answer by Andy
I suspect that you are missing the significance that the savings is in gallons, not miles. So consider gallons rather than miles per gallon.

Driver A drives, say, 12000 miles per year and gets 18 miles a gallon. 12000/18 = 666.66 gallons.
He buys a car that gets 28 miles per gallon, driving the same mileage. 12000/28 = 428.57 gallons
Gallons saved = 238.09

Driver B drives 12000 miles per year and gets 34 miles per gallon. 12000/34 = 352.94 gallons.
She buys a car that get 50 miles per gallon, driving the same mileage. 12000/50 = 240 gallons.
Gallons saved = 112.94

The function y = x is linear, but the function y = 1/x is non-linear. Gallons/mile is linear in gallons, but miles/gallon is non-linear in gallons.

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### One Response to Question: can you properly explain a problem concerning ratios and such?

1. Neil Kelcey

“The article points out how the majority of people believe that ➊ going from 34 MPG to 50 MPG saves more fuel than ➋ 18 MPG to 28 MPG, when this is in fact NOT the case.”

That is a true statement, and here is why:

The article is trying to make a case for the calculation for efficiency ratings be changed from miles per gallon to gallons per distance driven (it matters not whether it is gal/mile or gal/100mile)

Using the gal/distance method …

Case ➊:
34 miles per gallon is equivalent to 2.94 gallons per 100 miles

50 miles per gallon is equivalent to 2 gallons per 100 miles

So going from 2.94 gal/100 mi to 2 gal/100 mi is a 32.0% REDUCTION in the RATE of fuel consumption.

(2.94 – 2)/2.94 *100 = 32.0% (n. 10th)

Case ➋:
18 miles per gallon is equivalent to 5.56 gallons per 100 miles

28 miles per gallon is equivalent to 3.57 gallons per 100 miles

So going from 5.56 gal/100 mi to 3.57 gal/100 mi is a 35.8% REDUCTION in the RATE of fuel consumption.

(5.56 – 3.57)/5.56 *100 = 35.8% (n. 10th)

So Case ➋ IS, in fact, a better savings!

Using the (“traditional”) distance/gal method …

Case ➊:

The RATE of INCREASE of the # miles/gal from 34 to 50 is 47.1%

(50 – 34)/34 *100 = 47.1%

Case ➋

The RATE of INCREASE in the # miles/gal from 18 to 28 is 55.6% (n.10th)

(28 – 18)/18 *100 = 55.6%

.: calculating this way, case ➋ STILL wins!

So yes your mathematical instincts were right on … It DOES have something to do with ratios.

And this has been a good demonstration as to why percentages are a better way to judge numerical “situations” than people’s “perceptions” of truth.

Hope that helps you! Cheers! ☺

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