Today, on our way to the office, there was a huge traffic jam. I had tried solving this problem in the morning but was unsuccessful at it. I related the problem to Sanjeev and Sreepad, who immediately set about solving it. Since there was no paper to work out, Sanjeev started using his visiting cards. Sreepad, started doing it mentally. I had the road to mind, since I was driving, hence I sat and listened to the discussions. Sanjeev was the first one to crack it. Here is the solution.
(I am not giving the complete question here, since that would be some kind of copyright violation. Please buy "Problems in General Physics" by I. E. Irodov for the questions. Believe me, it is going to be money well spent)
The trick here is to change the frame of reference. Do not start making equations with earth as the frame of reference. Instead use the river. That is, our frame of reference moves with a velocity equal to the velocity of the river. Suppose the raft is at co-ordinates (0,0,0) at time zero. The boat travels for τ = 60 min and then turns and then travels back to reach the raft. The raft would still be at co-ordinates (0,0,0). Hence it would take exactly 60 min more for the boat to reach the raft. The boat thus takes 120 min or 2τ to reach the raft.
In the mean time the raft has travelled l = 6.0 km. Hence the speed of the river in km/min is,
v = l / 2τ
v = 6 / 2 * 60
v = 1 / 20 km/min
Converting to km/h,
v = 3 km/h