Nine minute fuse
Here is a puzzle I came up with after getting the wrong solution to one of Richard Wiseman's Friday puzzles.
You have all but finished setting up your very well timed fireworks display. All you have left is one kamuro shell for which you need to set a nine minute fuse. Unfortunately, all you have left are a few seven minute fuses and a few four minute fuses. Due to shoddy construction, these fuses do not burn at a constant rate - in fact, even two fuses of the same type might burn at different rates over different parts of the fuse. Is it possible to connect some fuses together (using a fuse glue which does not change burning time, of course) to get a fuse which will burn in exactly nine minutes? If so, how?
After completing your work, you find a super finally type firework that you want to use. Using only the four and seven minute fuses you have left, can you make a fuse that will burn for exactly nine and a half minutes? If so, how?