I got a lot of correct answers for this puzzle, and very happy to see this. Since the puzzle does not require any graphic for explaining the solution, I will just put the answer in text this time.
Answer for the second one: The trick here is to realize that you can measure 4 minutes by starting the two timers together and when the 7 minutes timer goes off, from that moment onwards until the 11 minute timer goes off, you have an interval of exactly 4 minutes. Once you are able to do that, you can use the 11 minutes timer again to reach 15 minutes. Therefore the answer is as follows:
(1) Start both timers together, (2) When the 7 minutes timer goes off, start boiling the egg, (3) Start the 11 minute timer again when it goes off, you have measured exactly 15 minutes
Answer to the First One: This is clearly trickier, though many people posted the answer correctly. There are two tricks to this puzzle: (1) Even though half the length of a fuse does not mean half the time to burn, if you light a fuse at both ends, the two sides will meet at exactly half the time, (2) You can light both the fuses also at the same time. Combining these two, here is the asnwer
(1) Light both sides of fuse #1, and one side of fuse #2
(2) When the two sides of fuse #1 meet, then 30 minutes have elapsed. At that time, light the other side of Fuse #2 as well
(3) Since 30 minutes were remaining in fuse #2 at the time fuse #1 fully burnt, it will take another 15 minutes for it to fully burn since it has now both sides lighted and you get 45 minutes.
Hope you enjoyed this!