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Let the length of race = x

When the first beat the second by 11 metres and the third by 90 metres, distance traveled by 2nd and 3rd horse at that time will be x -11 and x -90 respectively.

When the second beat the third by 80 metres traveled by 2nd and 3rd horse at that time will be x and x -80 respectively.

Ratio of speed of 2nd and 3rd horse = ratio of distance traveled = (x-11)/(x-90) = x/(x-80)

(x-11)*(x-80) = x(x-90)

By solving we get x = 880

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