Closest approach of two ships

Two ships move with constant velocities. Relative to a harbour \(O\), with distances in km, their position vectors \(t\) hours after noon are \(\mathbf r_A=t\begin{pmatrix}4\\ 3\end{pmatrix}\) and \(\mathbf r_B=\begin{pmatrix}10\\ -5\end{pmatrix}+t\begin{pmatrix}2\\ 5\end{pmatrix}\).

1. Find the speed of each ship.[2]
2. Show that the square of the distance between the ships at time \(t\) is \(8t^2-60t+125\).[2]
3. By completing the square, find the time at which the ships are closest and the least distance between them.[3]
4. The ships can communicate by short-range radio when they are at most \(4\) km apart. Find the length of time for which they can communicate, and state one assumption of the model that could make this answer unreliable.[3]