A toy pool table is $\quantity{6}{feet}$ long and $\quantity{3}{feet}$ wide. It has pockets at each of the four corners $P$, $Q$, $R$ and $S$. When a ball hits a side of the table, it bounces off the side at the same angle as it hit that side. A ball, initially 1 foot to the left of the pocket $P$, is hit from the side $SP$ towards the side $PQ$ as shown.
How many feet from $P$ does the ball hit side $PQ$ if it lands in pocket $S$ after two bounces?