Difficult# Velocities of Two Cars

CLMECH-QXUCFY

The motion of two cars is described by the following position vectors:

$$\vec {r}_1 = t \space (9 - t) \cdot \vec {i} + (t^2 - 10 \space t + 9) \cdot \vec {j}$$

and

$$\vec {r}_2 = (2 \space t^2 - 19 \space t + 9) \cdot \vec {i} + 2 \space t \space (t - 9) \cdot\vec {j}$$

...where $\vec {i}$ and $\vec {j}$ are the unit vectors in the $xy$ plane and $t$ is time. All the units are SI.

What are the magnitudes of the cars' velocities just before they collide?