Three runners A, B, C run a race, with runner A finishing 12 metres ahead of runner B and 18 metres ahead of runner C. In another race of same length, runner B finishes 8 meters ahead of runner C. Each runner travels the entire distance at a constant speed. The length of the race is :
Solution
Let A finish the race of: $x$ m
In same time, B runs : $x - 12$ m
And, C runs: $x - 18$ m ...(i)
In another race between B & C, B finishes the race of: $x$ m
In the same time, C completes: $x - 8$ ...(ii)
Ratio of speeds of B & C
$\Rightarrow \dfrac{x - 12}{x - 8} = \dfrac{x}{x - 8}$
$\Rightarrow (x - 12) (x - 8) = x(x - 18)$
$\Rightarrow x^2 - 20x + 96 = x^2 - 18 x $
$\Rightarrow 96 = 2x$ or x = 48 m