Grade 12: Optimal Driving Speed
How fast should we drive on the highway if we simply want to minimize our fuel costs for a fixed distance. The students are asked to figure out what the fuel consumption graph (litres/hour vs km/hour) looks like and then use graphical means to find the optimal speed. For the graph we are using it turns out to be 50 km/h.
Now we put a value of $6/h on our driving time (and a price on gas of $1/L) and use the same graphical solution to get 90 km/h.
Finally we move into the world of algebra and build a simple model for fuel consumption of a car, giving us a formula for our graph. Armed with that, both of our problems can be solved with some simple differential calculus.Teacher manual Student workbook