Timing nine minutes with 4- and 7-minute sand timers

You have two sand timers, one that runs for exactly $4$ minutes and one that runs for exactly $7$ minutes. Describe how to use them to time an interval of exactly $9$ minutes.

Start both timers together. At minute 4 turn the 4-minute timer over. At minute 7 the 7-minute timer runs out; turn it over. At minute 8 the 4-minute timer runs out, and the 7-minute timer has let through exactly 1 minute of sand; turn it over again and it empties at minute 9.