# The math in a hybrid car

For an end of the semester project in my physics classes, I posed the following question to my students:

If you put 100,000 miles on a car, which is a better deal, a hybrid or a traditional car?Students were asked to look up a car they would be interested in buying, but the car has to come in both hybrid and traditional engine models. They were asked to look at the price of the car and the cost of gas over the 100,000 mile “life” of the car (OK, some are going to sell it at 50K, and others hold onto it until it dies, but 10,000 seemed like a good average). We just finished a unit on energy, and I thought this would be a good way to get them thinking about energy and money.

If you want to know their results, you’ll have to keep reading, but I’ve since had time to think about making this question more open-ended, inquiry (thanks to Dy/Dan for keeping my on my inquiry toes). So now I’m thinking of the questions that could be raised in a class discussion:

- Write an equation for the cost of each car as a function of the miles driven.
- Using these two equations, solve for the intersection of the lines. What does this intersection represent?
- Car mileage is rated in both highway and city. Expand your equation to include a variable for the percent of driving that is city.
- How many extra fill-ups will it take to drive the traditional engine car? If your time is worth money, how much will this cost you if you make $50,000/year?
- How much gas is saved by driving the hybrid? What percent is this?

The list can go much further than this. Leave it up to your students to develop more.

Oh, the answer.Students did calculations from the Honda Civic to the Cadillac Escalade (yes, it comes in a hybrid). None of the hybrids broke even with the traditional engine in cost for 100,000 miles. Students were asked to write a short paragraph saying if they thought buying the hybrid was “worth it.” They gave great responses, including those who even looked at the gas they would save just from switching from the car they are now driving to a more fuel efficient car (one student said it wasn’t worth it to buy the hybrid, but certainly was worth it–financially and environmentally–to buy a new car to upgrade her mileage.

This is a blast, Lee. Thanks for emailing this to me.