Can we use math modeling and/or equations to answer the question of when it becomes advantageous to install a stoplight vs. a stop-sign? Can we “ambush” students by having them create equations without really knowing it?
What are some of the things we need to know about this?
- How long does a car usually stop at a stop-sign? And how long does it take to start up again?
- How long is the red light at a stoplight? Can we adjust this?
- What’s the time gap between a red-to-green light transition? A couple seconds?
- How long does it take a car to pass through an intersection?
- What’s the speed limit here?
- Have students use their iPhones or flip-cams to conduct some tests. For instance, here’s a couple of run-throughs through stop-signs in my neighborhood. Stopwatches at the ready! Improperly mashed-up music & driving video now!
(note: even though I’ve posted the videos, I would totally have students test it out on their own, hopefully with a stop-sign/light in their neighborhood that they find particularly ill-placed.)
(note: the speed limit WHICH I WAS DRIVING is 30 mph for this neighborhood, if that helps)
Each test took me about 10 to 15 seconds to slow down, come to a complete stop (as I’m sure all your students do) and then get back up to full speed. So it seems reasonable to assume that a stop sign will cause each vehicle about a 15 second delay, even if there are no cars around.
Potential Solutions and Possibly Foolish Assumptions
Assumption #1: It takes 15 seconds to go from full speed, to fully stopped, to full speed again.
If there were another car in front of us, there would be an additional wait time. Let’s say 10 seconds per car in front of us.
Assumption #2: We wait 10 seconds per each car that is also at the stop-sign.
Assumption #3: No matter the direction the other car is coming from, we wait 10 seconds to advance.
At this point, our equation may look like this:
Wait time for my car = (15 seconds) + (10 seconds) * (# of cars)
What about the total wait time for all cars? We’d have to multiply by the number of cars.
Wait time for all cars = (15 seconds)*(# of cars) + (10 seconds)*(# of cars)^2
Or, if we let y be the wait time for all cars and x be the number of cars,
y=15x + 10x^2
I’m going to cut things off and let you ponder this a bit. I’m sure I’ve made mistakes and false assumptions. I’m also going to let you guys think a bit about how we could represent the wait time for all cars at a stop light.
Couldn’t you see this sprawling into a really interesting Algebra project? Imagine students developing this model and bringing it to a community meeting or city planning gathering of some sort. It could happen.
Stay tuned for Part 2, and be sure to correct my math in the comments below!