When two particles meet again

Particles \(P\) and \(Q\) leave a fixed point \(O\) at the same time and move along the same straight line. After \(t\) seconds their velocities are \(v_P=6t-t^2\) m/s and \(v_Q=4+kt\) m/s, where \(k\) is a constant.

1. Given that the particles meet when \(t=6\), find \(k\), and find the other time at which they meet.[3]
2. Show that, for a general value of \(k\), the particles meet again at a time \(t>0\) only if \(t^2-\left(9-\dfrac{3k}{2}\right)t+12=0\).[2]
3. Find the exact range of values of \(k\) for which the particles meet again after leaving \(O\).[3]