A gentleman and his yacht

Logic Level 3

A gentleman with a top hat is taking a ride in his fabulous yacht in a long river. In still water, the yacht moves at a constant velocity \(v\). This can be affected by the direction and speed of the current. He sailed his yacht against the current of the river for 1 mile, at which point his hat blew off and landed in the river.

He didn't notice this for 30 minutes until it began to drizzle and he realized his hat must have blown off. Upon realizing this, he turned around, land embarked on a quest to retrieve his hat.

Amazingly, he reached the dock that he started from, at the same time his hat did! What was the rate of the current in miles per hour? (And yes, you have enough information)

This problem is not original.
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