Geometrical Application of Calculus with Speed Two vehicles are heading for a crossroad (point $C$) and intend to pass straight through.
Vehicle $A$ is $100\,\mathrm{km}$ due North travelling at $80\,\mathrm{km}/\mathrm{hr}$ towards $C$
Vehicle $B$ is $150\,\mathrm{km}$ due East travelling at $90\,\mathrm{km}/\mathrm{hr}$ towards $C$
Show that after time $t$, the distance $D$ between them is given by:
$$D^2=100(145t^2-430t+325)$$

Since the square function is strictly increasing on the non-negative reals, we might take $(D^2)'$ instead of $D'$, which is $100(290t-430)$.
