What is my MPG

Since my students rarely have the opportunity to see outside the prison walls they call home, I often enjoy using photography as a way to not only stimulate minds, but to also use as the basis for mathematics problems.

The premise of today’s problem is pretty simple. There are two photographs, one showing the gas gauge and odometer in the midst of my recent journey to Vermont, and the second, again displaying the gas gauge and odometer but this time at my destination. The only extra piece of information I will allow my students is the gas tank holds 20 gallons.

Photo 1: En route to destination

Photo 2: Arrival at Conference.

From these two photographs I developed the following set of questions:

1. How much gas did I use?
2. What was my miles per gallon?
3.  If I refilled the tank before heading home, how much would I spend if the gas station was charging $3.40

The mileage I travelled is readily available from the odometer. The difficult part of this exercise is determining how far the needle moved on the gas gauge. There are a couple ways of tackling this problem. I fired up GeoGebra and set as the background image both of these photographs side by side.

I used the circle through 3 points tool to complete the arc of the gas gauge, and then added a diameter through the needle on the gas gauge.

Gas Gauges with Circle and Diameter

By overlaying the circles, we can measure the angle the two diameters create. The other part we will have to do is estimate where the fuel gauge begins and ends. The last part will involve a bit of subjectivity.

Gas Gauges Overlay with Angles

I'll have a few of my geometry students tackle this problem this week and see how it goes. I will definitely pay attention to how they start the problem out, whether they will want printed copies or use computer software.