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Old 12-21-2013, 09:29 AM   #1
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Gas mileage quiz

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?
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Old 12-21-2013, 09:31 AM   #2
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Do you mean 10mpg and 20mph as a trick or is that a typo?
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Old 12-21-2013, 09:41 AM   #3
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A would save slightly more gas per mile.
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Old 12-21-2013, 10:04 AM   #4
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Do you mean 10mpg and 20mph as a trick or is that a typo?
yes...that was a typo. I meant mpg
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Old 12-21-2013, 10:14 AM   #5
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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.
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Old 12-21-2013, 10:51 AM   #6
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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...
Attached Files
File Type: pdf ChristmasPhysics.pdf (2.08 MB, 32 views)
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Old 12-21-2013, 11:02 AM   #7
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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.
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Old 12-21-2013, 11:06 AM   #8
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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).
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Old 12-21-2013, 11:11 AM   #9
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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.
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Old 12-21-2013, 11:16 AM   #10
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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.
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Old 12-21-2013, 11:22 AM   #11
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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.
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Old 12-21-2013, 11:27 AM   #12
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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.
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Old 12-21-2013, 11:48 AM   #13
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Quote:
Originally Posted by Texasdiver View Post
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!
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Old 12-21-2013, 12:10 PM   #14
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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?
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