Doing Calvin’s homework

Growing up, my siblings and I would read a lot of Bill Watterson’s Calvin and Hobbes. I have fond memories of spending hours reading and re-reading our grandparents collection during the school holidays. The comic strip is witty, heartwarming and beautifully drawn.

Recently, I came across this strip online

Originally published Feb 5th, 1990. You can read the rest of the story arc here:

Seeing Calvin take this test took me back to those school holidays. I remember grabbing paper and a pencil to work out the answer (I also remember getting teased by those previously mentioned siblings). Reading the strip years later, I realized there’s a neat way to work out the answer without having to write much down. Here’s the question again,

Jack and Joe leave their homes at the same time and drive toward each other. Jack drives at 60 mph, while Joe drives at 30 mph. They pass each other in 10 minutes.

How far apart were Jack and Joe when they started?

It can be hard to think about Jack and Joe traveling at different speeds. But we can simplify the problem by thinking from Joe’s perspective or frame of reference. From Joe’s frame of reference, he is staying perfectly still but Jack is zooming towards him at 30+60=90 mph. Jack reaches Joe in 10 minutes which is one sixth of an hour. This means that the initial distance between them must have been 90 \times 1/6 = 15 miles.

It’s not as creative as Calvin’s private eye approach but at least Susie and I got the same answer.