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?

If you change the puzzle to state that the boy and the girl start walking simultaneously, and the dog waits obediently for five minutes before taking off after them, then the puzzle makes more sense.

Boy's speed = 4mph = 0.07 miles/minute
Girl's speed = 3mph = 0.05 miles/second
Dog's speed = 10 mph = 0.17 miles/minute

After 5 minutes, the boy has gone 0.35 miles, the girl 0.25, and then the dog em"barks".

After another 2.08 minutes, the boy has gone to 0.35 + 0.07*2.08 = 0.50. The girl has gone to 0.05*2.08 + 0.25 = 0.35. The dog has reached the girl at 0.17*2.08 = 0.35

In the next 1.5 minutes, the boy goes to 0.50 + 0.07*1.5 = 0.61. The dog reaches the boy by going to 0.35 + 1.5*0.17 = 0.61. The girl gets to 0.35 + 1.5*0.05 = 0.43

Now the dog reverses course for the first time. He is 0.61 - 0.43 = 0.18 away from the girl, and trots to her at relative speed 0.17 + 0.05 = 0.22 miles/minute. It takes the dog 0.82 minutes to get to the girl. So now the boy is at 0.61 + 0.82*0.07 = 0.67. The girl and the dog are at 0.43 + 0.82*0.05 = 0.47.

Once again the dogged hound reverses course. In the next 2 minutes the dog goes to 0.47 + 0.17*2.00 = 0.81, where he meets the boy. The girl goes to 0.47 + 0.05*2.00 = 0.57.

Now the dog turns and heads for the girl. They are now 0.81 - 0.57 = 0.24 mile apart, which the dog covers at relative speed 0.17 + 0.05 = 0.22 miles/minute. This takes the dog 0.92 minute. Now the dog and the girl are at
0.57 + 0.92*0.05 = 0.62. The boy is at 0.81 + 0.92*0.07 = 0.87.

etc............

If I could write a program at this point, I would have the answer. (I will have Visual Basic on my desktop in a week or two. That should be interesting.)

Edited on January 24, 2004, 10:54 pm

Posted by Penny on 2004-01-24 22:47:48