Mind Games

Here's a puzzle for you:

Suppose you are a secret agent and you have been captured by your crazy arch-villain nemesis. Your arch-rival, being overly dramatic and not quite thinking his plan through, locks you in room. There is only one way in or out of this room and it is sealed by a vault door. Your nemesis informs you that the only escape is to turn the door latch in exactly 9 minutes. Turning the latch any time before or after 9 minutes will result in poison gas being pumped into the room, killing you. The only items in the room are two old-fashioned hourglass type timers, with the larger one counting down 7 minutes, the smaller counting out 4 minutes.

How do you know when to turn the latch?





Adapted from Vincent Janoski's post on the Geekdad blog.