Gap to the third-place car at the leader's finish

Three cars $A$, $B$, $C$ run one $1$ km lap at constant speeds. When $A$ crosses the line, $B$ is still $200$ m from it; when $B$ crosses the line, $C$ is still $200$ m from it. How far is $C$ from the finish when $A$ crosses?

360 m. $C$'s speed is $\tfrac{800}{1000}=0.8$ of $B$'s, and $B$'s is $0.8$ of $A$'s, so $C$ moves at $0.64$ of $A$'s speed. When $A$ has run $1000$ m, $C$ has run $640$ m, leaving $360$ m.