For the reaction, $5{\mathrm{Br}}^{-}+{\mathrm{BrO}}_3^{-}+6{\mathrm{H}}^{+}⟶3{\mathrm{Br}}_2+3{\mathrm{H}}_2\mathrm{O}$
If $-\frac{\mathrm{d}\left[{\mathrm{Br}}^{-}\right]}{\mathrm{dt}}={\mathrm{k}}_1\left[{\mathrm{Br}}^{-}\right],-\frac{\mathrm{d}\left[{{\mathrm{BrO}}_3}^{-}\right]}{\mathrm{dt}}={\mathrm{k}}_2\left[{\mathrm{Br}}^{-}\right]$ $\frac{\mathrm{d}\left[{\mathrm{Br}}_2\right]}{\mathrm{dt}}={\mathrm{k}}_3\left[{\mathrm{Br}}^{-}\right]$ then ${\mathrm{k}}_1,{\mathrm{k}}_2\text{ and }{\mathrm{k}}_3$are related as 

For the reaction, $5{\mathrm{Br}}^{-}+{\mathrm{BrO}}_3^{-}+6{\mathrm{H}}^{+}⟶3{\mathrm{Br}}_2+3{\mathrm{H}}_2\mathrm{O}$
         $\frac{-1}{5}\frac{\mathrm{d}\left[{\mathrm{Br}}^{-}\right]}{\mathrm{dt}}=-\frac{\mathrm{d}\left[{\mathrm{BrO}}_3^{-}\right]}{\mathrm{dt}}=\frac{1}{3}\frac{\mathrm{d}\left[{\mathrm{Br}}_2\right]}{\mathrm{dt}}$
       $\frac{1}{5}{\mathrm{k}}_1\left[{\mathrm{Br}}^{-}\right]={\mathrm{k}}_2\left[{\mathrm{Br}}^{-}\right]=\frac{1}{3}{\mathrm{k}}_3\left[{\mathrm{Br}}^{-}\right]$
or    $\begin{array}{l}3{\mathrm{k}}_1=15{\mathrm{k}}_2=5{\mathrm{k}}_3\\ {\mathrm{k}}_1=5{\mathrm{k}}_2=1.66{\mathrm{k}}_3\end{array}$