Question

In a race of three horses, the first beat the second by 11 metres and the third by 90 metres. If the second beat the third by 80 metres, what was the length, in metres, of the racecourse?

Accepted Answer

880. 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 $= \frac{L}{L-80}$. $\frac{L-11}{L-90} = \frac{L}{L-80} \implies (L-11)(L-80) = L(L-90) \implies L^2 - 91L + 880 = L^2 - 90L \implies L = 880	ext{ m}$.

Three Horse Race Course Length

Explanation

Practise this under exam conditions