SEOUL has the seventh largest subway system in the world, and will be the seventh most-populated city by the end of the decade.So why is it doubling its subway system? The simple answer is to get people out of their cars. Maybe. The number of vehicles in the city has quadrupled in 10 years, and more growth is expected; only 10 percent of people own a car. Rush hour, now almost a round-the-clock nightmare, has reduced the average speed of vehicles by one-third to 11 miles per hour, and that speed may be cut in half by the year 2000. Trips across the city that once took an hour can now take four. The estimated loss to the economy in wasted fuel and worker time is $2.12 billion each year, or about half the price of a new subway line. By 1999, four new lines will be added to the present four, with officials hoping to double the proportion of city travelers from the present 19 percent. By comparison, 76 percent of Tokyoites use rail. Why the boom in car ownership? "With the Olympics in 1988, people decided it was time to become more modern," says Chung Jong Hwan, chief of urban transportation in the Ministry of Transport. But then, he adds, Koreans discovered they were the worst drivers in the world, with 13,102 fatalities last year. "They are driving fast in a rude manner. Traffic culture is not established in this country. New drivers are overconfident," says Mr. Chung. Proposed solutions, such as higher taxes or incentives for carpooling, may not work. "In Korea, privacy is a very important factor in one's lifestyle. Carpooling will not be a popular option," Chung explains. Nor might the new subways get people to avoid driving, says Kang Hong Bin, Seoul's urban planner. He puts his hopes on two ring roads under way, and a proposed underground cross-city highway. Only 18 percent of Seoul is road, compared to 24 percent in Tokyo and 40 percent in Washington. Another plan to relieve traffic is a high-speed train between Seoul and Pusan, the second largest city. One idea that did not work was an experiment with double-decker buses. Too many bridges were too low. "It caused some safety problems," says Chung.