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.

**Question:**

How late was he, in minutes, to dinner (assuming he was on time before his adventure took place)?

**Note:**

The mathematician *is not* walking *in* the river at any point, but beside it.

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