Two pipes P and Q can fill a tank in $6$ hours and $9$ hours respectively, while a third pipe R can empty the tank in $12$ hours.  Initially, P and R are open for $4$ hours, Then P is closed and Q is opened. After $6$ more hours R is closed. The total time taken to fill the tank (in hours) is  ____
1. $13.50$
2. $14.50$
3. $15.50$
4. $16.50$