The Story of The Indecisive Rower

A rower rows regularly on a river, from A to B and back. He’s got into the habit of rowing harder when going upstream, so that he goes twice as fast relative to the water as when rowing downstream. 

One day as he’s rowing upstream he passes a floating bottle. He ignores it at first but then gradually grows curious about its contents. After 20 minutes of arguing with himself he stops rowing and drifts for 15 minutes. Then he sets out after the bottle. After some time rowing downstream he changes his mind, turns around, and makes his way upstream again. But his curiosity takes hold once more, and after 10 minutes of rowing upstream he turns and goes after the bottle again. Again he grows ashamed of his childishness and turns around. But after rowing upstream for 5 minutes he can’t stand it any longer, rows downstream, and picks up the bottle 1 kilometer from the point where he’d passed it. 

How fast is the current?

That's the speed of water current!

Water Speed in The Story of The Indecisice Rower

What was the story?

Just for a moment let's assume the rower is rowing on a calm lake where water is stationary. Then, the bottle that he saw is also not moving & floating at one point.

In the case, he moves away (upstream in real case) from the bottle & comes back (downstream in real case) again to collect the bottle. He rows away from the bottle for 20 + 10 + 5 = 35 minutes. 

Remember his speed is double when he goes away from bottle than when he is coming towards the bottle. That's why he takes 35 X 2 = 70 minutes to come back at the point where bottle is floating.

Moreover, he drifts for 15 minutes in real case; for that let's assume he sits motionless for 15 minutes (in our assumed lake case) at some point in between.

So after leaving the bottle, he returns to the bottle after 35 + 15 + 70 = 120 minutes.

Now, assume this water in the lake is moving and this bottle is 'displaced' by 1 KM away from it's original position in 120 minutes. 

That means, the water is moving at the speed of 1 km / 120 minutes. That is the speed of water current is 1/2 kmph.