It seems to me that at the instant the support car catches up to Carol two things happen:

1. The car and Carol have travelled the same distance, so .... (1)

2. The car and Carol are travelling at the same speed, so .... (2)

You need to solve equations (1) and (2) simultaneously for t and k .....

I get t = 5 seconds and k = 25/3 m/s (which is pretty quick! 30 km/hr ........)