A hat falls into a river, and its owner takes half an hour to notice. An essential piece of information seems to be missing, but a change of reference frame is enough.
The Hat in the Current
Riddle statement
A rower passes under a bridge while traveling upstream.
At that moment, his hat falls into the water, but he does not notice. He continues rowing upstream for 30 minutes, always at the same speed relative to the water.
He then notices the loss, turns around immediately, and rows downstream at that same speed relative to the water.
He catches up with the hat exactly 1 kilometer downstream from the bridge.
How fast is the current flowing?
Show solution
Solution
Let us observe the scene from the water's reference frame. In that frame, the hat remains where it fell.
The rower moves away from it for 30 minutes. He then turns around and returns at the same speed relative to the water. Because he must cover the same distance at the same speed, he takes another 30 minutes to reach it.
Exactly one hour therefore passes between the fall and the recovery of the hat.
During that hour, the current carries the hat 1 kilometer downstream. Its speed is therefore:
1 km ÷ 1 h = 1 km/h.