You have a string-like fuse that burns in exactly one minute. The fuse is inhomogeneous, and it may burn slowly at first, then quickly, then slowly, and so on. You have a match, and no watch. How do you measure exactly 30 seconds?
Regardless of the pace at which the fuse burns at any given position on, the two flames will meet at the 30 second mark. For example, if the 90% of the string takes 30 seconds to burn, it means the last 10% also takes 30 seconds. Lighting from both ends means the flame will meet at the 10%/90% position on the string, but this occurs after 30 seconds.