What saves more gas?

[iago]

This is from Seth Godin's blog (I won't post a link because it has a spiler).
--
Let's say your goal is to reduce gasoline consumption.

And let's say there are only two kinds of cars in the world. Half of them are Suburbans that get 10 miles to the gallon and half are Priuses that get 50.

If we assume that all the cars drive the same number of miles, which would be a better investment, and why?
    * Get new tires for all the Suburbans and increase their mileage a bit to 13 miles per gallon.
    * Replace all the Priuses and rewire them to get 100 miles per gallon (doubling their average!)
--

[deadly7]

This is from Seth Godin's blog (I won't post a link because it has a spiler).
--
Let's say your goal is to reduce gasoline consumption.

And let's say there are only two kinds of cars in the world. Half of them are Suburbans that get 10 miles to the gallon and half are Priuses that get 50.

If we assume that all the cars drive the same number of miles, which would be a better investment, and why?
    * Get new tires for all the Suburbans and increase their mileage a bit to 13 miles per gallon.
    * Replace all the Priuses and rewire them to get 100 miles per gallon (doubling their average!)
--

Bumping the 10 up to 13. These cars are the bottleneck in terms of gas usage. As it is, the Priuses don't take that much gasoline in comparison (even on a 50 mile trip, they use a gallon compared to five gallons of a Suburban), so upgrading them just means you're making the good better. You still have the low floor created by the dysmal Suburban gas mileage.

I can post an actual solution later if this doesn't satisfy you, but I'm a bit busy now.

[iago]

This is from Seth Godin's blog (I won't post a link because it has a spiler).
--
Let's say your goal is to reduce gasoline consumption.

And let's say there are only two kinds of cars in the world. Half of them are Suburbans that get 10 miles to the gallon and half are Priuses that get 50.

If we assume that all the cars drive the same number of miles, which would be a better investment, and why?
    * Get new tires for all the Suburbans and increase their mileage a bit to 13 miles per gallon.
    * Replace all the Priuses and rewire them to get 100 miles per gallon (doubling their average!)
--

Bumping the 10 up to 13. These cars are the bottleneck in terms of gas usage. As it is, the Priuses don't take that much gasoline in comparison (even on a 50 mile trip, they use a gallon compared to five gallons of a Suburban), so upgrading them just means you're making the good better. You still have the low floor created by the dysmal Suburban gas mileage.

I can post an actual solution later if this doesn't satisfy you, but I'm a bit busy now.

An actual solution is cool, but not necessary.

The point of this is actually that the answer is counter-intuitive to most (not counting math people, of course :P). Ask that to an average person, and they'll almost certainly get it wrong.

[rabbit]

Are we ignoring the fact that more gasoline is used to assemble a Prius than a suburban or not?

[iago]

Are we ignoring the fact that more gasoline is used to assemble a Prius than a suburban or not?

It isn't in the problem, and the problem is a closed system (a hypothetical world).

[deadly7]

So, a [hopefully correct] mathematical solution:

The variables:
Let x be Gallons of Gas Needed to Travel 50 miles (the maximum mpg amount in this case problem)
1. At factory defaults
1a. Suburban=5x
1b.Prius=x

2. Now let us upgrade the vehicles:
2a. Upgrade a Suburban. Suburban=5x. Suburban'=5/(1.3/1)x=5/1.3x . So add Suburban'+Prius=5/1.3x+x=6.3x/1.3. So 6.3/1.3~4.85 gallons of gasoline to travel 50 miles in each car.
2b. Upgrade a Prius. This means Prius=x and Prius'=0.5x . Suburban=5x . So add Prius'+Suburban=5.5x . So 5.5 total gallons of gasoline to travel 50 miles in each separate car.
3. 4.85x <<< 5.5x so it's more efficient to upgrade tires, neglecting all other factors.

[Camel]

There was a push a while back to switch to gallons/thousand-miles as the standard. Never caught on.

[Joe]

What I, as a normal person, would think is that 10:13 (1:1.3) is a much lower ratio than 50:100 (1:2), so the Prius would be a much better upgrade option.

[rabbit]

What I, as a normal person, would think is that 10:13 (1:1.3) is a much lower ratio than 50:100 (1:2), so the Prius would be a much better upgrade option.

Too bad it's wrong.  The question is overall economy, not which benefits more, since it's pretty obvious that individually, the stupid fashion accessoryPrius benefits more in a side-by-side comparison.

[deadly7]

What I, as a normal person, would think is that 10:13 (1:1.3) is a much lower ratio than 50:100 (1:2), so the Prius would be a much better upgrade option.

Clearly you can't read. Look at my post.

[Blaze]

What I, as a normal person, would think is that 10:13 (1:1.3) is a much lower ratio than 50:100 (1:2), so the Prius would be a much better upgrade option.

Clearly you can't read. Look at my post.

He's saying an average person would be to stupid to know what you said.

[Towelie]

There was a push a while back to switch to gallons/thousand-miles as the standard. Never caught on.

If you look at that its easy to tell which is a better option.
          (before/after)
Prius:         20/10   gal/thousand miles
Suburban: 100/~77 gal/thousand miles

So... you save 23 gallons of gas per 1000 miles with the Suburban compared to 10 with the Prius, which is 2.3x more!

[Chavo]

Best efficienty-gain answer with lowest cost is to convince everyone that drives a Suburban to /wrists

[Camel]

convince everyone that drives a Suburban to /wrists

+1

[Quik]

Best efficienty-gain answer with lowest cost is to convince everyone that drives a Suburban to /wrists

But then you're left with a world of douchey Prius drivers!