Fisherman saling up stream and drops cork travels back .

[teddyayalew]

Homework Statement

A fisherman is sailing up-stream; when passing under a bridge, he drops a boat-hook in the water. After half an hour he discovers this, turns back, and overtakes the boat-hook 5km below the bridge. What is the speed of the current if the fisherman rows at the same speed up and down the river?

Homework Equations

x=vt

The Attempt at a Solution

I have drawn the diagram to visualize what is going on
http://i40.tinypic.com/2qvtdop.jpg

and defined certain equations
http://i42.tinypic.com/34ir8fq.jpg

I understand that the hook traveled 5km downward along along the stream after
30min +xmins but I am having trouble figure out how to solve for x so that I may solve for the velocity of the stream

 

[tms]

Homework Statement

A fisherman is sailing up-stream; when passing under a bridge, he drops a boat-hook in the water. After half an hour he discovers this, turns back, and overtakes the boat-hook 5km below the bridge. What is the speed of the current if the fisherman rows at the same speed up and down the river?

Homework Equations

x=vt

The Attempt at a Solution

I have drawn the diagram to visualize what is going on
http://i40.tinypic.com/2qvtdop.jpg

and defined certain equations
http://i42.tinypic.com/34ir8fq.jpg

It would be easier on your readers if you included your equations in the body of the post.
You should also write down all equations.

I understand that the hook traveled 5km downward along along the stream after
30min +xmins but I am having trouble figure out how to solve for x so that I may solve for the velocity of the stream

The first step in solving any problem is to write down the equations, and to do this you will have to define some variables. So, let $v_{r}$ be the speed the fisherman rows at wrt the water, and let $v_{c}$ be the speed of the current. Let $t_u$ be the time the fisherman rowed upstream, let $t_d$ be the time the fisherman rowed downstream, and let simple $t$ be the total time. Let $x_h$ be the distance the boathook floated downstream. You may need some more variables.

Now let upstream be the positive $x$ direction, and let the bridge be $x = 0$.

Now write down equations for the fisherman's trip and for the boathook's trip. From those you should be able to see how to solve the problem.

 

[teddyayalew]

Thank you so much I was able to arrive at the right solution. I found that
TIME(u) = TIME(d) so then V(c) * (TIME(u) + TIME(d)) = V(c) * one hour

and we know the cork traveled 5km during the total time so
V(c) *one hour = 5km ,,, V(c) = 5km/hour!