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The Hat and the River (Posted on 2003-05-05) Difficulty: 4 of 5
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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Solution Laborious solution | Comment 19 of 24 |

v= water speed
V= boat speed relative to the water
t=0 is time that hat falls off
t=5 minutes is time boat turns around
t=T is time hat and boat arrive at original starting point

Formula:  d=r*t

At t=0, hat begins its one mile journey at speed v, so v*T=1 mile
At t=5 minutes, boat begins its journey back down the river:
    boats speed relative to land is now V+v
    travel time of boat downstream is T-5
    distance boat travels is:  I don't know yet, let's figure it out
Distance boat travels upstream after losing hat:  
        (V-v)*5minutes  [since boat speed relative to land is V-v]
So, while boat goes downstream: 
(V+v)*(T-5) = 1mile + 5(V-v)
VT + vT - 5V -5v = 1 + 5V -5v      but remember vT=1
VT + 1 + 1 + 10*V
T=10 minutes
Hat goes 1 mile in 10 minutes
Hat speed = v = water speed = 6 MPH.

  Posted by Larry on 2004-12-28 22:47:51
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