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?
Explanation:
Let x be the length of the racecourse.
The first horse beat the second by 11 metres and the third by 90 metres.
∴ Distances travelled by the first, second and third horse are x, x − 11 and x − 90 respectively.
The second horse beat the third by 80 metres.
Distances travelled by the second and third horse are x and x − 80 respectively.
Ratio of speeds of second and third horse is constant which is equal to the ratio of the distances travelled by the second and third horse.
∴ (x − 11)/(x − 90) = x/(x − 80)
⇒ x2 - 91x + 880 = x2 - 90x
⇒ x = 880
Hence, 880.
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