Driving - Miles Per Hour

This video has gone viral recently and reminded me of a funny incident of doing some quick math in my head to win a bet.  You might have seen this.  If not, take a peek!

This is probably how I'd react to simple questions about Harry Potter or Star Wars (no, I've never seen either - unleash your insults in the comments), so I empathize.  But this emphasizes thinking of such a common label (MPH) in a different way.  Oh yeah, 80 miles per hour means 80 miles traveled in one hour (or 60 minutes)!

So one night I was driving a bunch of high school kids back home from an away football game.  We were a long distance from home, and I told Jeff, who was riding shotgun, that I'd tell him the exact time we'd get off the interstate.  He wanted to bet something on it, so I told him a Coke.  I told him we'd get off the interstate at 12:18am.  Sure enough, when we reached our exit, the time was 12:18am!  I never made Jeff pay up, but he and I still talk about it and laugh 5 years later as our first real interaction!  So how did I do it?

It has to do with this miles per hour thing, along with the fact that the mile markers on the interstate are a mile apart.  Here was my thought process: We were driving 70mph.  That's 70 miles per 1 hour, aka 70 miles/60 minutes.  Reducing the fraction, that's 7 miles/6 minutes.  That's a ratio.  You could also write the ratio 6 minutes/7 miles.

I knew this route very well.  Here's the diagram.  Upon approaching the Mile 80 marker, I subtracted and saw we had 47 miles to I-75 and 17 miles to exit, so 64 miles left.  I knew that I was going to take either 7/6 or 6/7 of 64.  Since I'm going over 60 miles/hour (a mile per minute), I know it's going to take less time than 64 minutes.  Multiplying by 6/7 makes sense since multiplying by a fraction less than 1 makes it smaller (6/7 < 1).

64 divided by 7 = 9 1/7.  Multiply by 6, and I get 54 6/7 (fractions are better than decimals*, just sayin'), or almost 55 minutes to get there from that point!

So when approaching the Mile 80 marker, it was 11:23pm and I made the bet!

Of course, I was driving and could ensure we stayed around 70 mph.  If we got behind someone slow, I could speed up later. :)  Try it on a long trip sometime!  Maybe you could win some favors or a Coke!  But make sure you do the math right and start figuring it out a couple miles ahead of time to be ready to make the wager.  Try it by yourself first.

Notes:

Mathematically, you could set up a proportion.  6/7 = x/64 and solve for x.

If going 60mph, it's simple.  64 miles in 64 minutes

If going 75mph, 60min/75miles = 4/5.  Multiply distance by 4/5.

If going 80mph, 60min/80miles = 3/4.  Multiply distance by 3/4.

Don't feel the need to speed up to 120mph just to multiply by 1/2!

And wear your seatbelt, be responsible, and all that. :)

What you learn in class that applies:

1. Ratios

2. Being mindful of labels

3. Multiplying fractions

4. Reducing fractions

5. Comparing fractions (6/7 < 1 and 7/6 > 1)

6. Solving proportions

I wonder if anyone else has tried something like this besides me.

*Fractions are exact.  Decimals are not always exact. 1/7 is .142857 repeating.