Start both timers at the same time. Once the 7-minute timer is empty, flip it. Four minutes later, the 11 minute timer will be empty, but only 4 minutes of sand will have emptied from the 7-minute timer. So, if you flip the seven minute timer just as the 11-minute timer empties, it will only have 4 minutes of sand in the top. That is a total of 11+4 = 15 minutes.