A boy, a girl and a dog are standing together on a long, straight road. Simultaneously, they all start walking in the same direction: The boy at 4 mph, the girl at 3 mph, and the dog trots back and forth between them at 10 mph. Assume all reversals of direction instantaneous.

In one hour, where is the dog and in which direction is he facing?

It is not clear to me how all three can start walking simultaneously from the same starting point (the puzzle says they are initially standing together) in the same direction, and the dog still be trotting back and forth between the boy and the girl. The dog is faster than the boy, so by the time the boy has gotten any distance ahead of the girl, the dog will be ahead of him. So when does the dog initially embark (no pun intended), and when does he start trotting back and forth? Is there some subtle calculus here that escapes me?
Edited on January 24, 2004, 8:05 pm

Posted by Penny on 2004-01-24 20:02:59