Tim has to exactly time a quarter of an hour. For this he uses two fuses, which both burn for exactly one hour—but not evenly. This means that half of a fuse is not necessarily burned after exactly half an hour.
How does Tim manage to exactly time 15 minutes with the two fuses?
Tim must light one fuse at both ends and the other at one end only. When the first fuse has burned down, he knows that the other one has to burn for another half hour. By lighting the other fuse at the second end as well, he can shorten this time by half and therefore time exactly 15 minutes.