${{A}_{A}}{{v}_{A}}={{A}_{B}}{{v}_{B}}\Rightarrow \frac{{{v}_{A}}}{{{v}_{B}}}=\frac{{{A}_{B}}}{{{A}_{A}}}={{(\frac{{{r}_{B}}}{{{r}_{A}}})}^{2}}={{(\frac{1}{3})}^{2}}=\frac{1}{9}$