Today's lesson is looking at bicycle gears as an application problem for direct and inverse variations. I bring in my bike and put it on a stand so that it's easy to rotate the pedals and have the wheels turn. I give them the following handout (because I learned last year that it takes some students a really long time to copy down a table and that wasn't the best use of their class time even though it was more friendly to our budget).
This turns out to be an inverse variation. We then leave the rear sprocket alone and change the front sprocket, and then do the same thing.
In 2005 Lance Armstrong won the Tour de France for a record seventh time. Over the course of the race, his mean (average) speed was 41.7 km/h.I really like this activity, but last year I felt like the students didn't really "get" it completely. I've simplified a few things and provided them the table (which gives us some extra time), so I'm hoping that helps, but I'm open to any brilliant suggestions on how to make sure they understand it.
a) Find his mean (average) speed in ft/sec.
b) It took him 86 hours, 15 minutes and 2 seconds to complete the Tour de France. How many feet did he go?
If you're interested in cycling, then you might be interested in these videos - The Science of Cycling (part 1, part 2, part 3).