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.)

(In reply to re(2): General Shortcut Formula by Jayaram S)

Ok this problem's solution does not hold water speed with me.

Let's say we know the water speed to be 1 mile/minute.

Let's say that "full throttle" of the boat is 2 miles/minute.

Now following these equations, he heads up the river for 5 minutes at this speed of 2 -1 or 1 mile/minute. d=v/t so the distance is 5 miles.

Now downstream, to the exact same point in which we started heading at a velocity of 2 + 1 or 3 miles/minute. You will find we reach that point in the equation t = d/v or 5/3= 1.67 minutes!

So the total time to reach our exact same point is 6.67 minutes, and we could reach the campsite 1 mile away in 7 minutes.

Therefore my conclusion is what? This arguement makes no sense. This problem is unsolvable, because the answer varies with the speed of the boat, and the speed of the river!

If we assume as told, "(Assume that he travels the same speed the entire time and that there is no turn around time.) ", then we can at least arrive at a general solution, that is pretty close to the answer.  Let Vr be the velocity of the river.

Vr= 1 mile/ time

Now, the time is equal to 5 minutes one way, and 5 minutes back to the spot he lost his hat. Now, he still has one mile to get back to the point where he meets his hat back at the campsite. That time can ONLY be found with a known speed of the boat. So, I leave the Vr as a dependent variable on Vb, the velocity of the boat.

Vr = 1 mile / ((1/Vb) + 10 minutes)

You will note that the velocity comes out roughly, yet not quite exactly, to the posted solution or about 6 miles/ hour for most speeds of the boat. 

Edited on December 28, 2004, 4:58 am

Posted by Michael Cottle on 2004-12-28 04:55:29