The first time SpongeBob and Patrick meet is when they have run a combined distance equal to the circumference of the track, which is 1/2 km. Every time they meet after that, they will have run a combined distance equal to the circumference of the track plus the distance they have already run. Since they are running in opposite directions, their combined speed is 15 km/hr + 10 km/hr = 25 km/hr. Let's call the distance SpongeBob has run when they meet for the 30th time "d":
d = 25 km/hr x time
We know that they will have met 29 times before the 30th time they meet, so the combined distance they will have run before the 30th time they meet is:
(29 x 1/2 km) + (29 x d)
We can set this equal to the total distance SpongeBob and Patrick will have run before the 30th time they meet:
30 x 1/2 km
Simplifying this equation gives:
29 x d = 15 km - 14.5 km
Solving for d gives:
d = 0.017 km
Therefore, SpongeBob has run 0.017 km when they meet for the 30th time.