[Bungleau]

Jeez... it's a bummer for the first response to be the correct one. Thought I'd found a tricky one... guess not.

But let me respond back...

Start both hourglasses. When the four-minute hourglass is empty, flip it. Elapsed time four minutes, and three minutes worth of sand left in the seven minute hourglass.

When the seven minute hourglass is empty, flip both. Incremental time is three minutes, for an elapsed time of seven minutes. One minute of sand left in the four minute hourglass, and seven minutes in the now-flipped seven minute hourglass.

When the four minute hourglass empties, flip the seven minute hourglass. Incremental time is one minute, for a total of eight minutes. Seven minute hourglass now has one minute of sand on top, and six on the bottom.

When the seven minute hourglass is empty, you will be at nine minutes.