# Driving to grandma's puzzler

I did indeed read the article you linked to. You said “I still don’t think there is a precise way to measure logs to this day.” A precise way to measure logs is by weighing them. I am right, you are wrong. I don’t care how wood is SOLD. You were talking about measuring. And could the method you described be any MORE inaccurate?

Oh, now you want to divide a dollar EQUALLY? You couldn’t bring yourself to type the word “equally” in your original post? That argument remains irrelevant and is dismissed based on your poor presentation.

While I would take whatever exam the college of my choice required (I don’t know about you corn folk out in Iowa, but I took both SAT and ACT and performed splendidly. I was disappointed with my performance on the LSAT (how networking relates to law, I’ll never know… networking the math subject, that is.))

Your main point is solid. The person drove two distances at two known speeds. That’s all one needs to know.

I love it when people try to average speeds this way. Let’s consider an extreme case:

You’re driving a round trip to your other Grandma’s, and you’ve decided you want to average 50 mph for the whole turnaround. But there’s bad weather, bad traffic, dead armadillos littering the road, you drop your cellphone and spend ten minutes pulled off to the side of the road fishing it out from under the seat… Anyway, you do a little preliminary math when you get to Grandma’s place, and find that you’ve averaged only 25 mph so far. How fast do you have to drive the return trip to make up for the delays and realize the original goal of 50 mph overall average?

Seven people out of ten will say 75 mph will do it, because averaging 25 and 75 gives you 50.

Two more out of ten will think, aha! I averaged half the desired speed coming up, so I need to average twice the speed going back; I gotta drive 100 mph!

All nine of those people are wrong.

First off, the distance to Grandma’s is irrelevant. All that matters is that the distance back is the same (which, unless you’ve got some alternate-route thing worked out, is going to be the way it works). Fact of the matter is, you can’t do it. Not at 75, not at 100, not at 1000 mph. Not unless you can teleport yourself and your car instantaneously back to your starting point. No matter how fast you drive on the return trip, the average speed for the round trip is going to be below 50 mph.

And the street-corner explanation is that speed is “distance divided by time”. To average 50 mph, you have to cover both legs of the trip in some amount of time, and if you did 25 getting to Grandma’s, you’ve used up all the time already.

And that, gentlemen, is why pit crews practice and practice getting fuel in a car and the tires changed in seconds.

Funny thing, everybody insists on driving 5 to 10 mph over the speed limit on the freeway yet you almost never see anyone run to their cars in the parking lot as fast as they can run.

You’ve posed a different puzzle, which you made unsolvable as a demonstration by cherry-picking the numbers. It doesn’t relate to the Puzzler at hand. Why don’t you submit it to the show? It was a worthwhile exercise… I spent a full two minutes thinking about it.

The puzzle posed by dadoctah is just taking the principle of the show’s puzzler to an extreme.
The distance you cover while going zero mph is always zero miles, no matter how much time you spend going zero mph, so you can not get a correct average by averaging distance at speed. You have to average time at speed.

This is also why the professional road racers will gladly give up a couple of mph top speed on the straights if it means going 1 mph faster through the slowest turns on the race track.
My Garmin GPS calculates average speed and displays a running estimated time of arrival. Stopping to pee will set back the ETA by at least 5 minutes even if there is no line for the restroom. You have to speed 10 over the limit on the freeway for a long, long way to undo the ETA setback caused by the pee stop.