Bob is having a nice camping/fishing trip along a river. He leaves his campsite early in the morning, and gets on his boat, heading full throttle upstream.

After going for exactly one mile, his hat flips off of his head, and starts floating downstream. Bob doesn't realize that his hat has fallen off for five minutes, but then he notices that it's missing, and turns full throttle downstream.

He finally catches the hat at exactly the same spot as he camped that morning. The question is, how fast was the water traveling?

(Assume that he travels the same speed the entire time and that there is no turn around time.)

Actaully, what is really requied for a solution is three indpendant or orthagonal pieces of information - hence 3 equations, three unknowns.  Threre are systems of 3 equations and 3 unknonws that do not have a unique solution sicne they represent the same "information":

Ex:  1x + 1y=1, 2x+2y=2, 3x+3y=3.  There are infinite solutions, so long as x+y=1.

In this case the three orthogonal pieces of info are:

The hat takes T miniutes to get back to the campsite and so does the boat

The boat goes 5 minutes upstream and turns around, with he boat and water speed being constant (except for direction of the boat)

The hat goes exactly 1 mile

This is why there is a unique solution.

 

 

Posted by Kenny M on 2005-12-10 13:42:32