I have two seemingly contradictory lines in my book regarding crossing a stream. Point IV below says the time to cross over to the other side doesn't change if there is a current as the increased distance is compensated by increased speed. But Point V seems to suggest that the two times t and t' are different.
Can anyone please tell me where is my logic wrong? I just fail to see it. If t and t'are same, won't the speed of current be zero by that formula? How are the two cases different?
I believe IV is the case where the man swims directly across the river with respect to the water. On the other hand, V is the case where he swims directly across the river in the ground frame (He swims at a slight angle to balance the drifting effect of the current).