Car Race Distance

Let the total distance of the race be $D\text{ km}$. When car A finishes $D\text{ km}$, car B has covered $D - 45\text{ km}$ and car C has covered $D - 90\text{ km}$. The ratio of speeds of B and C is: $\frac{V_B}{V_C} = \frac{D - 45}{D - 90}$ Also, when car B finishes $D\text{ km}$, car C covers $D - 50\text{ km}$, so: $\frac{V_B}{V_C} = \frac{D}{D - 50}$ Equating the two ratios: $\frac{D - 45}{D - 90} = \frac{D}{D - 50}$ $(D - 45)(D - 50) = D(D - 90)$ $D^2 - 95D + 2250 = D^2 - 90D$ $5D = 2250 \implies D = 450$ Hence, the race distance is $450\text{ km}$.