Gas mileage quiz

[Texasdiver]

I teach HS physics and here is a question I threw onto this week's final exam related to the concept of efficiency.

You have two vehicles that you drive equal distances each year; a truck that gets 10 mpg and a car that gets 20 mph. You want to achieve the greatest gas savings but you can only afford to replace one vehicle. Which choice will save the most gasoline?

A. Replace the 10 mpg truck with a new 15 mpg truck
B. Replace the 20 mpg car with a new 50 mpg car
C. Both choices will save the same amount of gasoline
D. It is impossible to know from the information given.

Guess which answer most students put down?

[SteveSueMac]

Do you mean 10mpg and 20mph as a trick or is that a typo?

[Lumatic]

A would save slightly more gas per mile.

[Texasdiver]

Originally Posted by SteveSueMac

Do you mean 10mpg and 20mph as a trick or is that a typo?

yes...that was a typo. I meant mpg

[Texasdiver]

Originally Posted by Lumatic

A would save slightly more gas per mile.

Most people immediately pick B thinking that a 30 mpg increase in the car is worth much more than a 5 mpg increase in the truck. But there is a huge law of diminishing returns when it comes to gas mileage. We and the media are obsessed with mileage at the high end...thinking that it is meaningful for example if the new Prius gets 55 mpg instead of the 50 that the old one gets. When the real savings are to be had with vehicles at the other end of the range.

If we take a 50 mpg Prius and through extreme technology raise its gas mileage to 100 mpg that saves exactly 1 gallon of gas for every 100 miles driven.

If we take a 9 mpg truck and raise its gas mileage to 10 mpg that saves 1.1 gallon of gas for every 100 miles driven.

This is also why I think an efficiently streamlined airstream trailer is a such a better choice than a big boxy high-profile 5th wheel for high mileage use. The total fuel savings are so much greater when you can make small improvements at the lower end.

I see lots of discussion on these forums about how many years it takes to pay back a higher investment in a diesel vs gas engine. One could also do the same thing comparing a 5th wheel to an airstream in terms of fuel efficiency. A one or two mpg difference in trailer hauling can add up to a LOT of fuel over say 20,000 miles.

[TX_Streamer]

It's enticing to pick the choice that more than halves the rate of fuel consumption. But Pickup #1 gets so poor economy, any increase is a large bump.

So, was it A or B? With little confidence in today's youth, I'd normally say they picked B. But that would be a slight on your teaching skills.

I posted my solution to your problem...my inner science nerd is beginning to show...

[SteveH]

I think it's impossible to compute because even though you do state you drive both vehicles the same distance, you don't state what that distance is, or how many miles.

Any amount of computing will be based on an assumption that probably is not true.

[Texasdiver]

Originally Posted by TX_Streamer

It's enticing to pick the choice that more than halves the rate of fuel consumption. But Pickup #1 gets so poor economy, any increase is a large bump.

So, was it A or B? With little confidence in today's youth, I'd normally say they picked B. But that would be a slight on your teaching skills.

I posted my solution to your problem...my inner science nerd is beginning to show...

You did it algebraically and of course correctly. Here is a simple math way to solve it:

Assume all 4 vehicles drive 100 miles.

The 10 mpg truck drives 100 miles and uses 10 gallons of gas (100 miles / 10 gallons). The 15 mpg truck drives 100 miles and uses 6.67 gallons (100 miles / 15 mpg). Total fuel savings by switching trucks is 3.33 gallons (10 gallons - 6.67 gallons)

The 20 mpg car drives 100 miles and uses 5 gallons of gas (100 miles / 20 mpg). The 50 mpg car drives 100 miles and uses 2 gallons of gas (100 miles / 50 mpg). Total fuel savings by switching cars is 3.00 gallons (5 gallons - 2 gallons).

[Texasdiver]

Originally Posted by SteveH

I think it's impossible to compute because even though you do state you drive both vehicles the same distance, you don't state what that distance is, or how many miles.

Any amount of computing will be based on an assumption that probably is not true.

Doesn't matter whether you drive one mile or a million miles. Choice A will always save more gasoline.

[Texasdiver]

By the way, the A students tended to actually solve the math and pick the correct answer A. The B/C/D/F students tended to not do the match (or do it incorrectly) and tended to pick B. Hardly any students picked C or D.

Overall more students picked the incorrect answer B. Had I actually given them a review with a similar problem on it more would have gotten it right simply because they would have remembered it was a trick question. This was more out of the blue to see if they could solve a problem they hadn't exactly seen before.

[SteveH]

Originally Posted by Texasdiver

Doesn't matter whether you drive one mile or a million miles. Choice A will always save more gasoline.

Guess I would have failed the class.

[msmcv51]

Your question is which answer did most of the students put as the correct one. That would be a pure guess on our part. My answer to the question would be to replace the truck. Let us assume that they are both driven 10,000 miles. The new truck would use 333.3333333333 less gallons per year. The new car would use only 300 gallons less per year. That is only about $125 per year difference. Now if the new truck would cost $12,500 more than the new car than it would take 100 years to justify the higher cost new truck to save the 33 gallons of gas per year.

[TX_Streamer]

Originally Posted by Texasdiver

Here is a simple math way to solve it:

Assume all 4 vehicles drive 100 miles.

The 10 mpg truck drives 100 miles and uses 10 gallons of gas (100 miles / 10 gallons). The 15 mpg truck drives 100 miles and uses 6.67 gallons (100 miles / 15 mpg). Total fuel savings by switching trucks is 3.33 gallons (10 gallons - 6.67 gallons)

The 20 mpg car drives 100 miles and uses 5 gallons of gas (100 miles / 20 mpg). The 50 mpg car drives 100 miles and uses 2 gallons of gas (100 miles / 50 mpg). Total fuel savings by switching cars is 3.00 gallons (5 gallons - 2 gallons).

True, but I have had it hammered into my head to always solve the general case first. Never solve a proof by example!

[HiHoAgRV]

If you want to take it to the next level, add in the value/cost of the vehicles.

Is a paid for vehicle that has no trade in value, gets 20 mpg and is driven 650 miles a week, better than a 45 MPG vehicle with a $450/Mo note?

[m.hony]

Originally Posted by HiHoAgRV

If you want to take it to the next level, add in the value/cost of the vehicles.

Is a paid for vehicle that has no trade in value, gets 20 mpg and is driven 650 miles a week, better than a 45 MPG vehicle with a $450/Mo note?

I would say yes.
It isn't just the note- it is also the difference in insurance and license cost.
We buy/finance a vehicle when we are backed up against a wall and have no other alternative- or when upkeep and maintenance starts to average $300-350 a month-
I used to stand on my soap box and proclaim I would never have a car note. I ate those words. If you pay over $300 per month maintenance on some piece of junk you can't depend on to go around the corner you still have a piece of junk with a broken air conditioner. If you pay $350 per month for a new car, you have a new car-
Flip side- if your paid for vehicle costs $500-1000 per year in maintenance you are way ahead. My 1999 Nissan Pathfinder was averaging $450-500 per year maintenance. That was fine. It has crept up to averaging $1,500 per year in maintenance. I keep hoping maintenance costs will be less next year, but it doesn't happen. I still think it's cheaper to keep 'er- at least for now. Even a $2500 engine or transmission repair beats a $25,000 replacement car in my book.
Another option is to get a newer/more reliable daily driver and use the older car as a back up/plan B. I am currently thing about a used Lexus RX330- won't tow the 'Stream, but it will tote the family.

[m.hony]

It is funny to me that people will justify a new car purchase with fuel economy- to keep from putting $50 per week of gas in your 1973 Oldsmobile, you go get a $500 car payment on a new car to pay $25 per week in gas...huh? That just don't make no sense- to me, anyway.

[nickmeloy]

Originally Posted by Texasdiver

...

You have two vehicles that you drive equal distances each year; a truck that gets 10 mpg and a car that gets 20 mph. You want to achieve the greatest gas savings but you can only afford to replace one vehicle. Which choice will save the most gasoline?
...

If the typo was also on the final exam, then the answer would be insufficient information. Was it on the exam, and did anyone question the information?

[Texasdiver]

Originally Posted by nickmeloy

If the typo was also on the final exam, then the answer would be insufficient information. Was it on the exam, and did anyone question the information?

The exam was correct. I typoed when I typed it into this forum posting screen on my iPad

[Grrrwolf]

But for arguments sake, if you are still using the other vehicle the same amount, wouldn't B be the better choice?

Example:
Replace A; Ave of 15mpg & 20mpg per number of miles
Replace B; Ave of 10mpg & 50mpg per number of miles

[Texasdiver]

Originally Posted by Grrrwolf

But for arguments sake, if you are still using the other vehicle the same amount, wouldn't B be the better choice?

Example:
Replace A; Ave of 15mpg & 20mpg per number of miles
Replace B; Ave of 10mpg & 50mpg per number of miles

You can't average them because the relationship is not linear. Fuel consumption goes up geometrically as you approach zero and at zero mpg your fuel consumption becomes infinite.

For example,

The 10 mpg vehicle drives 100 miles and uses 10 gallons
The 50 mpg vehicle drives 100 miles and uses 2 gallons

You have used a total of 12 gallons to drive 200 miles. Your combined fuel economy is therefore 16.67 mpg (200 miles divided by 12 gallons) and not 30 mpg which is the average of 10 and 50.