Speed of hat = speed of water

Upstream 10min = (water purification speed-water flow speed) × 10.

The hat is gone 10 minute = water speed × 10.

Their distance difference = (water purification speed-water flow speed) × 10- water flow speed× 10 = water purification speed×10.

Downstream speed when people chase = still water speed+current speed

The speed difference between man and hat = water purification speed+water speed-water speed = water purification speed.

Distance difference ÷ speed difference = clear water speed × 10÷ still water speed = 10 minutes.

The hat has gone 10+ 10 = 20 minutes.

Water velocity 1000 ÷ 20 = 50m.

You don't have to answer so complicated. I'm afraid you don't understand and write so much.