It should not take very long at all (Less than a minute) . The sea water pump picks up the water. Its then routed to an oil cooler then to the engine and exhaust. Very simple in design. Sounds like you better check the sea water pump. Rebuild kit is only $80. If you find the rubber impleller is wasted, do not forget to back flush the system to get all the parts out. Very import step some people forget.
Go spend the money and buy the proper water attachment($20) and ditch the tub