Turn over both hourglasses at once. When the four-minute hourglass runs out, turn it over. When the seven-minute hourglass runs out, turn it over. When the four-minute timer runs out this time (eight minutes have elapsed), the seven-minute hourglass has been running for one minute. Now turn over the seven minute timer back over. When the timer runs out, nine minutes have elapsed.
To see more past Problem of the Week's refer to the Riddles Newsletter annals.