How Do You Calculate River Flow Velocity in a Kinematics Problem?

[LHC_23]

Homework Statement

A motorboat going downstream overcame a raft at a point A;
• = 60 min later it turned back and after some time passed the raft
at a distance l = 6.0 km from the point A. Find the flow velocity
assuming the duty of the engine to be constant.

Homework Equations

---------------------------------

The Attempt at a Solution

I assumed the stream velocity as v₀ and the velocity of the motorboat with respect to water as v^' . The motorboat reached point B while going downstream with velocity (v₀ + v^') and then returned with velocity (v^' - v₀) and passed the raft at point C . Then I assumed t to be the time for the raft to move from point A to C , during which the motorboatboat moves from A to B and then from B to C .

But after this I have no idea how to proceed .
Pls Help!

 

[N-Gin]

Let $$v_{0}$$ be the velocity of the stream, $$v$$ velocity of the motorboat, $$t_{0}$$ time after the motorboat changes direction (60 minutes) and $$L$$ distance form point A (6 km).

After 60 minutes, distance between boats is

$$d=vt_{0}.$$

At that moment, motorboat is at point B. After time $$t$$ passes, the boats meet at point C. So, they travel their own distances in the same time interval $$t$$. Therefore

$$d=vt_{0}=v_{0}t+(v-v_{0})t.$$

And we also know

$$L=v_{0}(t+t_{0}).$$

$$v_{0}$$ is easy to obtain from those equations.

 

[AC130Nav]

Homework Statement

A motorboat going downstream overcame a raft at a point A;
• = 60 min later it turned back and after some time passed the raft
at a distance l = 6.0 km from the point A. Find the flow velocity
assuming the duty of the engine to be constant.

Homework Equations

---------------------------------

The Attempt at a Solution

I assumed the stream velocity as v₀ and the velocity of the motorboat with respect to water as v^' . The motorboat reached point B while going downstream with velocity (v₀ + v^') and then returned with velocity (v^' - v₀) and passed the raft at point C . Then I assumed t to be the time for the raft to move from point A to C , during which the motorboatboat moves from A to B and then from B to C .

But after this I have no idea how to proceed .
Pls Help!

But the motorboat is only an observer, otherwise irrelevant. The raft traveled 6 km in 60 minutes.