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 The Hat and the River (Posted on 2003-05-05)
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.)

 See The Solution Submitted by Jonathan Waltz Rating: 2.0000 (4 votes)

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 Puzzle Solution Comment 24 of 24 |

Let s = the distance that the hat traveled floating down stream.and:
t = the time for which the boat traveled upstream (in hours) without Bob noticing the fallen hat.

Then, it follows that when Bob's hat was lost s miles upstream, thenceforward the hat's motion relative to the water current was stationary.

Now, after losing the hat, Bob's speed in the water is constant (as before losing his hat), and the hat's motion relative to the water is stationary. Thus, since Bob took t hours to notice the Hat's loss, it also took him a further t hours in pursuit and discovery of the hat.

Now, in these t+t = 2t hours, the hat has move a distance of s miles with the water current.

accordingly, the speed of the water current  = s/(2t).

Now, it is given that: (s,t) = (1, 1/12), and consequently:

The water was moving at a speed of (12/2) = 6 miles per hour.

 Posted by K Sengupta on 2008-11-17 23:52:07

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