Three students $A$, $B$, and $C$ are traveling from a location on the National Highway No. $5$ towards Hanoi to participate in the HOMC 2018. Initially, $A$ takes $B$ on the motorcycle, while $C$ rides the bicycle. After one and a half hours, $B$ switches to a bicycle and immediately continues the trip to Hanoi, while $A$ returns to pick up $C$. Upon meeting, $C$ continues the travel on the motorcycle to Hanoi with $A$. Finally, all three students arrive in Hanoi at the same time. Suppose that the average speed of the motorcycle is $50$ km per hour and that of both bicycles is $10$ km per hour. Find the distance from the starting point to Hanoi.

Let's think step by step and output the final answer within \boxed{}.
user