Points $A$, $B$, $C$ and $D$ are chosen on a line in that order, with $AB=9, BC=4$. Equilateral triangles $APB$, $BCQ$ and $CDR$ are constructed so that $P$, $Q$ and $R$ are on the same side with respect to $AD$. If $\angle PQR=120^\circ$, and the length of $CD=\frac {a}{b}$, where $a$ and $b$ are co-primes, determine $a-b$.