On intersections of locally quasiconvex subgroups

Let $H_1,H_2$ be locally quasiconvex, torsion-free subgroups of a hyperbolic group $G$. We prove $\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{k}(H_1\cap H_2)$ can be bounded in terms of $\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{k}(H_1)$ and $\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{k}(H_2)$.