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