Question 40

Three runners A, B and C run a race, with runner A finishing 12 m ahead of runner B and 18 m ahead of runner C, while runner B finishes 8 m ahead of runner C. Each runner travels the entire distance at a constant speed. What was the length of the race?


Let x be the required distance.

Let a,b,c be speed of the A,B and C respectively.

From the given conditions we have, 

$$\frac{a}{b}=\frac{x}{x-12}$$ and $$\frac{a}{c}=\frac{x}{x-18}$$ and $$\frac{b}{c}=\frac{x}{x-8}$$ . From first 2 equations we can deduce $$\frac{b}{c}=\frac{x-12}{x-18}$$. 

$$\frac{b}{c}=\frac{x-12}{x-18} = \frac{x}{x-8}$$

x = 48 satisfy the equation.

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