How much time is saved by increasing speed?

I was driving from Montreal to Halifax this summer. The speed limit on the highway in New Brunswick and Nova Scotia is 110km/h, but I've heard that this is + or - 10 km/h, therefore cops don't stop you if you are driving up to 120km/h.

Anyway, I was driving and driving (it's a 13h drive). At one point, my whole family was sleeping, so I had nothing better to do but to think. I thought of many silly things, but one of them was math related. As you might realize, I wanted to get to Halifax as quickly as possile, therefore was trying to figure out how much time I would save if I went 5km/h faster than I was at the time.

I was trying to do this in my head ("mental math"), and I thought it would be a simple calculation. I knew that it depends on the distance, and how much I increase my speed. But with these two variables, I wasn't getting reasonable numbers. I then realized, that it also depended on the speed I was driving at the time. For instance, if I was driving 110km/h initially, and was planning to drive 115km/h, then that would give a different result if I was driving 120km/h and increased my speed to 125km/h. I was so dissapointed with my "mental math" abilities, and I actually almost grabbed a pen and paper and started working on the problem on paper (while driving), but then I realized that the problem could wait until the hotel room, and that the safety of my kids and husband was more important than solving a silly problem.

In the hotel room I quickly figured out the formula - problem solved. By the way, the time saved is not very large at all - not worth it.

But this might be a fun real math example in class: possibly a question on a test, for homework, or a discussion in class.

Note: For an easy question, lower level of math or physics class you might want to give the specific speed you are going at initially and how far you still need to go, but for a more challenging question, you might want to ask the students to figure out a general formula for the decrease in time in terms of the initial speed.

If you don't know how to do this yourself, you can contact me, and I'll fill you in on the secret, although if you're teaching math or physics this is really not all that difficult.