After they start, the speed at which the cars are moving toward each other is (30 mph) + (20 mph) = 50 mph. At the time they meet, Car A will have traveled 30/50 = 0.6 of the distance around the track, while Car B will have traveled the other 0.4 times the distance.
Car A will have to cover only 0.4 times the length of the track before being at the start. This is 0.4/0.6 = 2/3 of the distance Car A has already traveled, so is expected to take 2/3 of the time already taken.
Car B must cover 0.6/0.4 = 3/2 times as much track as it has already covered. In order to do so, its speed will need to be
... speed ratio = (distance ratio)/(time ratio) = (3/2)/(2/3) = 9/4
times what it has been so far.
Car B's speed will need to be
... 9/4 × 20 mph = 45 mph
to finish at the same times car A does.
