How to measure 15 minutes using sandglasses of 7 minutes and 11 minutes?

#
It is possible to flip the hourglasses at the moment when not all the sand has run out.

## Solution

Let the first hourglass be for 7 minutes, and the second for 11 minutes. We will start both hourglasses.

First method. After 7 minutes, we will flip the first hourglass, and then after another 4 minutes, that is, when all the sand in the second hourglass has run out, we will flip the first hourglass again. At this moment, the sand in the first hourglass will have 4 minutes worth of sand at the bottom, and 3 minutes worth at the top. Therefore, by flipping the first hourglass, we can measure another 4 minutes.

Second method. After 7 minutes, that is, when all the sand in the first hourglass has run out, there will be 4 minutes worth of sand left at the top of the second hourglass. From this moment, we start the countdown. As soon as all the sand in the second hourglass has run out, we will flip them and measure another 11 minutes.