The hat that fell in the river

Question

A canoeist is paddling upstream at a steady effort. As he passes under a bridge his hat falls into the water, but he does not notice. Ten minutes later he realises, turns round immediately, and paddles downstream with the same effort until he catches up with the hat. He reaches it one kilometre downstream of the bridge. How fast is the river flowing? You are not told the canoeist's speed.

Accepted Answer

Three kilometres per hour. Ride along with the water. Imagine floating on a raft that drifts with the current. From the raft, the hat is stationary: it just sits on the water. The canoeist, paddling with the same effort in both directions, moves away from the hat at some speed s for 10 minutes, then turns and moves back towards it at the same speed s. Going back takes exactly as long as going out: another 10 minutes. So the hat was in the water for 20 minutes in total. Back on the bank. In those 20 minutes the hat drifted with the current from the bridge to a point 1 km downstream. So the cur…

The hat that fell in the river

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