Although, peachykeen, yours is the only answer anyone can understand, nine min. could be timed a bit faster using a similar method.
-Start both timers
1. When the 4 min. glass is done, start it again. (The 7 min. glass now has 3 min. left to count)
2. When the 7 min. glass is done, start it again. (There will be one min. remaining on the 4 min. glass and the 7 min. glass will now be counting that one min.)
3. When the 4 min. glass is done, the 7 min. glass will now have just one min. worth of sand on the bottom, turn it over and that sand will count the remaining min.
1. 4min. (from the 4 min. glass)
2. 3min. (from the 7 min. glass)
3. 1min. + 1min. (the first from the 4 min. glass, the second from the 7 min. glass)
We're trying to time 9 minutes! How can that ever be done faster than in exactly 9 minutes, huh? None of the methods could ever claim to be faster than any of the others. They could at best be simpler to use, simpler to understand even.
In that respect, b.t.w., your method wins by all means. Very clear, and easy to understand. Even for me