A bus, a train, and a plane depart at the same time from city $A$ to city $B$. If I take the bus, whose average speed is $100~\mathrm{km}/\mathrm{h}$, I will arrive at city $B$ at 8 PM. If I take the train, whose average speed is $300~\mathrm{km}/\mathrm{h}$, I will arrive at city $B$ at 2 PM. What will be the arrival time of the plane if its average speed is $900~\mathrm{km}/\mathrm{h}$?