"A man is rowing upstream (both the man and stream move at constant rates). As he passes under a bridge, he accidentally drops his hat in the water, but doesn’t realize it until he has rowed for 10 more minutes. He then turns around and rows downstream, retrieving his hat 1 mile beyond the bridge. How fast is the stream flowing?"
Man drops hat in stream.
Man rows against the current for 10 minutes.
Distance rowed is unknown, as is rate.
If we knew at least one, we could calculate the other.
So far things are going badly.
Man rows with the current unknown distance for unknown time at an unknown rate. We know only that he has gone at least one mile and probably further if had made any progress going upstream.
If this man had only checked the velocity meter on his rowboat at critical points, we wouldn't be in the mess we are in now.
So how fast is the current going?
Your guess is as good as mine.