Two hour glasses brain teaser. See above.
Sigiloso
Turn both hour glasses over at the same time. When the 7 minute hour glass is done there will be 4 minutes left on the other hour glass. Turn this one over (this is that start of the 15 minutes). Once the 4 minutes has drained, immediately flip it back over and let the 11 minutes drain. This will give you the 15 minute time you need.