[Azred]

Originally posted by Faceman: And a funny one (this one I stole from a book and did not think up myself): A hunter and his dog are returning home. When they are in sight of their cabin (about a mile away) the dog starts running towards the cabin at 18mph while the hunter continues to walk at 3mph. When the dog arrives at the cabin he turns around and runs back to the hunter (who is now nearer tothe cabin) only to turn around again once he reached his owner and make a run for the cabin. He continues runninng back and forth between hunter and cabin until the hunter arrives at the cabin. How much distance did the poor dog cover?

The hunter moves at 1/6 the rate of the dog, so everytime the dog runs towards the cabin the hunter covers 1/6 of that distance. When the dog runs back, the distance from the cabin to the hunter must be split into 7 equal parts; the dog covers 6 and the hunter covers 1. So when running back, the hunter goes 1/7 of the distance from his previous position to the cabin.
What you get is a 2-step iterative process beginning with position 0 at time 0. At time 1 the dog is at position 1 and the hunter is at 1/6. At time 2, they meet at 1-((1/7)*(1-1/6)) = 2/7. Now the loop begins, because the dog runs 1-(2/7) and the hunter moves (1/6)*(1-(2/7)), placing him at (2/7)+(1/6)(5/7)=(17/42). The repeated second step shows the dog runs (6/7)*(1-(17/42)) and meets the hunter at 1-((6/7)*(1-(17/42)))=(24/49).
In the end, by continuing the process and adding the distances run by the dog: 1 + 2(5/7) + 2(25/49) + 2(218/343) + ... = 6 miles.

I presume daan is thinking of displacement, which compares the distance between the dog's starting and ending positions. [img]graemlins/petard.gif[/img]