How long does it take to get US from South Korea by Container Ship?

It is presently not possible to travel from S Korea to the US, or anywhere else, via freighter. Since the Sewol sinking, Korea has restricted embarkation for passengers on freighters, as reported to me by 4 different cargo travel agencies as of April 2016. I'm presently awaiting a CMA CGM vessel in Hong Kong, which was the next closest option. Ironically, we will be in Busan to load and offload cargo, though I am not permitted to leave the ship in that particular port. From Busan, that leg of the Columbus Loop is 12-14 days to Seattle, depending. Other ships on the Pearl River Express make a similar crossing to Long Beach, CA in about 12 days.

I've had excellent luck directing specific enquiries to Hamish Jamieson of Freighter Travel NZ, who's operated these sorts of voyages for quite a number of years.