The price of gas is going up tomorrow. Should I go fill up my tank?
Why?
- Illustrate the human factor that complicates apparently simple math problems
- Discussion of sustainability in transportation
- Practical application of linear relations, unit conversions
- Facilitates critical thinking
This is the dilemma:
You are at home in the evening and you hear on the news that the price in gas is going up 5 cents over night. You know you will need to fill up soon anyways. You are faced with a choice: Go out now to fill up or just go on the way into school/work tomorrow morning. You know if you go now, there will probably be a line at the pumps. How much will you save if you go tonight? Is it worth the inconvenience?
I know most high school students don't drive so it might not be a great question for them. Or maybe its a calculation they can share with their parents. Regardless, it's a question I have wondered whenever I hear gas prices are going up and I see line ups of cars at gas stations.
From my calculations, I would save about $2.00 to fill up 50L by driving out to the gas station. Assumptions listed below and will vary by model of car and other factors:
- Fuel Efficiency = 10L/100km (from the dashboard display on my parents' car)
- Distance to Gas Station = 1.5 km
- Idling consumption = 0.1 L /10 minutes (I found this on one site. Very unsure about the accuracy)
- Assume a 10 minute line up for gas (idling) before the price goes up
- Assume a fill up is 50 L
In a class...
Because most likely a lot of students won't have vehicles of their own, I would probably present them with the above scenario and results. Really, the point of this would be to start a deeper discussion about how we often oversimplify decisions like this. This activity could really be done in any Science class. It's a valuable lesson on how complicated Real-World Problem Solving and decision making can be.
I would pose this question to them:
Given the fact that you will save $2.00 if you fill up tonight (instead of tomorrow), will you go fill up?The first instinct may be to be purely economical and say yes of course. Maybe students could look at trends in gas prices over the year and see how often big price drops/increases occur to try to predict how much they would save over a whole year.
Challenge the Assumptions
I would expect students to inquire about how I got the $2.00. I would then explain my method to them and they could further critically analyze the assumptions I used to arrive at the answer. Something that may come up is the gas consumption unit of L/100 km (or MPG in the States). Where does that measure break down? Idling! When you are idling, the gas consumption should theoretically be infinity L/100 km because you aren't going anywhere but are still using gas but most cars that report 'instantaneous' fuel consumption in the console will show 0 L/100 km. If you calculate the average fuel consumption using the instantaneous values, the average will be biased downwards because of this. So what do car companies report when they advertise efficiency? I don't know. Something to discuss!
Time is Money
I would then challenge them a bit and ask how much them how much their time is worth to them. This is something they would not think about if they don't have a job. Say it takes 25 minutes to drive to the station, wait in line, fill up, and return home. Is it still worth it? Quantifying how much a persons time is worth is an interesting topic (engineers use it when optimizing public transit routes and schedules). For a high school student, would they consider minimum wage ($10.25) to be how much their time is worth? If so, the 25 minutes it takes is not worth it! It also depends on how busy they are. Do they have an exam coming up the next day? Or are they not doing anything anyways? The Human Factor can complicate things.
Internalize the Externalities
What about the environmental implications of going out to fill up? How much carbon dioxide is released during the trip and while idling? Idling is actually very inefficient on gas and produces a relatively large amount of CO2 for not moving anywhere. This is a good way to get into discussions about the impacts of elevated greenhouse gases and the carbon tax debate. We pay for water, electricity and gas. If we are using up clean air by polluting it, why aren't we paying for that as well?
According to Wikipedia, the Energy Density of Gasoline is 36 MJ/L. I calculated 0.4 L of gas for the trip to the gas station and back. Thats 14.4 MJ or 4 kWh - the equivalent of leaving a 40 W lightbulb on for about 4 days. In terms of energy used, it's not insignificant (though it would only cost about 40 cents of electricity because our electricity is ridiculously cheap). This highlights how much energy transportation actually uses. Remember, that the 14.4 MJ is only for driving 3 km and idling for 10 minutes.
21C...
Students could weigh all these options and come to conclusions which they can share with the class or discuss in a discussion board. The topic can be used as a jumping off point for a whole host of STSE issues as well.
Okay so maybe this is a bit of a mundane way to illustrate the complexity of problem-solving and decision making that doesn't demonstrate 21C all that well. There are probably much better examples of cost-benefit analysis (such as the Exploding Ford Pinto Debacle), but I was curious about filling up the tank before the price goes up so that's what I decided to write about.
2. Knowledge Construction: entry - adoption - adaptation - infusion - transformation
3. Real-World Problem Solving & Innovation: entry - adoption - adaptation - infusion - transformation
3. Real-World Problem Solving & Innovation: entry - adoption - adaptation - infusion - transformation
- Ethics in Engineering and problem solving/decision making
- Optimal vehicle speed for fuel efficiency/GHG emissions
No comments:
Post a Comment