Three points, $A, B$ and $C$ travel along a straight line, each having the same origin.
Points $A$ and $B$ travel in the same direction at a speed of $5$ km/hr and $10$ km/hr, respectively. Point $C$ traverses between points $A$ and $B$ at a speed of 15 km/hr. Whenever $C$ reaches to $A$, he starts to move back to $B$, then again move back to $A$. After $1$ hour, how far from the origin is $C$ located?
I have no solution to the problem, this is a spin-off from a much easier problem.
Note: I have changed the original of the question to make it solvable and interesting. (Oray)