Gently down the stream
A mathematician is walking home along the bank of a river at \(1.5\) times the speed of the current, which flows in the opposite direction to his line of motion.
He is carrying a stick and a hat. With the noble purpose of throwing his stick into the river, he accidentally throws his hat. After a while, he notices his mistake, throws his stick into the river and runs back after his hat at \(3\) times the speed of the current, which is now flowing in his direction of motion. He catches his hat, immediately turns around and starts walking back in the intial direction at his intial speed. In \(10\) minutes he meets his stick.
How late was he, in minutes, to dinner (assuming he was on time before his adventure took place)?
The mathematician is not walking in the river at any point, but beside it.