Because the runway loop is 400 meters, Party A and Party B start at the same time. Assuming that the time is X, the distance traveled by Party A in X time is 490X, and the distance of Party B is 250X, and the difference between them is (490-250) X. When Party A and Party B meet for the first time, they should be exactly one lap apart, that is, Party A is faster than Party B, so the equation is X = 400 (490. When A and B meet for the second time, they should be just two laps apart, that is, A is two laps faster than B, so the equation is X=800(490-250), and then X= 10/3 (minutes).

Then, the first meeting was 1 minute 40 seconds, and the second meeting was 3 minutes 20 seconds.