Puzzler Answer: Cruisin' to Grandma's House

RAY:This was one in our inexhaustible series of mathematical puzzlers. And it bears a striking resemblance to the other mathematical puzzlers we use.

TOM: Different?

RAY: A little different, just a little twist. There was this young gal who had had a couple of pretty bad accidents, so her grandmother gives her a large sum of money with which to buy a brand new Volvo, a nice safe car. The only condition is that when she gets the car, grandma wants to see it to make sure that she didn't run out and buy a Firebird. So on the first available Saturday, she drives to grandma's house which is 120 miles away.

And of course I'll mention that these kinds of puzzlers always assume that she lives right on the highway, and so does grandma -- there's no time lost accelerating, da, da, da, you know.

Because she's not particularly eager to get there, she sets the cruise control for 40 miles an hour and drives the 120 miles to grandma's house. In fact, the car even has one of those little trip computers that has a little display that says, "Your average speed is 40 miles an hour." Now, she doesn't want to spend too much time with the old grandma -- because she'll start asking about her boy friends and all that stuff -- so she hangs around for a while, shows grandma the car and leaves.

On the way back she sets the cruise control for 60 miles per hour. She travels the same road, the same 120 miles, and when she gets home she does a little figuring. She says, "Let me see, I drove 120 miles up and 120 miles back, so that's 240 miles. And 40 miles an hour, and 60 miles an hour on the way back, my average speed was 50 miles an hour, so it should have taken me 4.8 hours, right? That's 240 divided by 50 which is the average speed and it comes out to 4.8.

TOM: Oh.

RAY: But it took 5 hours.

TOM: Really.

RAY: How can that be?

TOM: Certainly did, three and two is five.

RAY: Three and two is five, how can it be? Well, she didn't calculate the average speed; she calculated the average of the speeds.

TOM: Yeah, a common mistake.

RAY: In fact, her average speed is not 50 miles an hour but it's really 48 miles an hour. And you arrive at that by calculating the total distance divided by the total time. The total distance being 240 miles, and the total time we already know.

TOM: So it's 240 divided by five hours.

RAY: Which comes out to be --

TOM: 48 miles an hour.

RAY: Anyway who's our winner?

TOM: The winner is Herbert Nelson from Chicago, Illinois.

[ Car Talk Puzzler ]