On June 25, 1950, the Korean Warbegan when North Korea, supported by the Soviet Union and China, invaded South Korea, which was supported by the United States. General MacArthur, leader of the United Nations forces, drove the North Koreans back across the divide, yet encountered a Chinese invasion.
Basically, the U.S was a fellow supporter of south korea, and that's how they got included.
Before people relied on their own skills of hunting/gathering to survive, now people developed tools and methods to utilize nature into what they need ie farming, cross breeding, livestock before it was always moving to where animals were to hunt or plants now one could settle anywhere if they know methods to farm and breed
The distance between the two areas is somewhere around 2300 miles although it's difficult to say with high degree of precision. Richard traveled with his army over the course of 2 years, but this was faster than most armies did since it could last as much as 3 years for an entire army to travel so far. In smaller groups, it would be possible to cover this area in a year.