Express t from one equation and substitute in into the other.
Yes. Also, you probably got that t = 9 / (4 - a). The latter graph looks like this. So, for a > 4 the time to meeting is negative, which means that the meeting must have been in the past and will not happen in the future (this is natural since if B moves right faster than A, they cannot meet). For a < 4, the function t(a) is increasing. Since we need to find the smallest t, we need to find the smallest allowed a.
Since the maximum speed of B is 8 km/h, the vector (a, b), when its beginning is at (0, 0), lies inside a circle of radius 8. Also, b= -2a+7. The circle carves a segment on the line b = -2a+7, and we need to take the left end of that segment, which corresponds to the smallest a.