Three Horse Race Course Length

Let racecourse length be $L$. When 1st finishes ($L$), 2nd covers $L-11$ and 3rd covers $L-90$. Ratio of speeds of 2nd and 3rd $= \frac{L-11}{L-90}$. When 2nd finishes ($L$), 3rd covers $L-80$, so ratio $= \frac{L}{L-80}$. $\frac{L-11}{L-90} = \frac{L}{L-80} \implies (L-11)(L-80) = L(L-90) \implies L^2 - 91L + 880 = L^2 - 90L \implies L = 880\text{ m}$.