Solve Relative Motion: Boat, Wood + River Flow

[Kamataat]

Hi, I have this exercise that I've been trying to do for a couple of days now. Can anybody help me? Here's the question:

A boat is moving against the direction of flow of a river and meets a piece of wood that is moving along with the river. The boat continues against the flow of the river for another 30 minutes and then turns around. Moving at the same speed relative to the water as before, it catches up with the piece of wood 3km from the place where they met. What was the speed of the river?

Answer: 3 km/h.

I've tried setting up all sorts of equtions of motion relative to Earth (the place where they met), but haven't been successful at getting the right anwer. Should I set up the equations in terms of the point where the boat turns around?

- Kamataat

 

[Chi Meson]

This is a problem that is to be solved by thinking, not by plugging into an equation.

From the reference point of the water surface, the piece of wood has NOT MOVED, has it?

From the reference point of the surface of the water, the boat has moved away for 1/2 an hour at a certain speed, and then returned at the same speed. Its the same distance at the same speed, so it must be the same time interval. It therefore must have been a full hour of travel for the boat.You got it from there?

 

[Kamataat]

Yes, thank you. I was thinking of everything relative to the Earth when I should have just taken the boat's speed relative to the water as a hint that everything should be seen in relation to the water being stationary.