logical deduction - Doubt : Pokemon Hunter and the Rogue Brook

I was working my way through some Puzzles in Discrete Maths by Rosen, when I came across the following question:

• A Pokemon Hunter is rowing upstream a brook
  


• As he passes under the 'bridge-of-curse', he throws a Pikachu into the brook
  



• 5 minutes later, he realises that Pikachu will die and he should not have done that
  He rows back and picks Pikachu 3km. downstream of the 'bridge-of-curse'
  

What is the speed of the river flow?

My Answer:

- Distance : 3km
- Time : 5 minutes + 5 minutes ( due to the stream's frame of reference ) = 10 minutes
- Speed = 3000 / 600 m/s = 5 m/s

Doubt:

Am I correct ? Seems a bit too easy ...

Answer

You assume it takes him 5 minutes back as well. Here is a sketched solution:

s = speed of stream
r = speed of rowing in water with no current
t = time since drop to pickup

We have:

s * t = 3 // Pikachu travelled 3 kilometers for that time
t = 3 / s

We also have:

(t - 5) * (r + s) = 5 * (r - s) + 3

Which means the distance travelled returning is the distance going away + 3 kilometers. From here on we have:

(3 / s - 5) * (r + s) = 5 * (r - s) + 3
3r/s - 5r + 3 - 5s = 5r - 5s + 3
3r/s - 5r = 5r

10r = 3r/s
10rs = 3r
10s = 3

s = 10/3 = 3.3333 kilometres per minute

s = 3/10 = 0.3 kilometres per minute

This seems quite fast to me, if you see a typo in my calculations, feel free to edit or comment. Note $t =10$ which matches your assumption.