I'm not going to solve the problem, but I'll help outline the approach you should take.
In the first case, with the flat road, you have a car moving in a circular path due solely to centripedal force. The force is solely supplied by static friction. (Side note: Why static and not kinetic? The car is not sliding through the turn. If the car starts to skid, that means that the tires have exceeded the maximum static frictional force and now kinetic friction applies.) So, based on the geometry of the situation, you should be able to derive what you need from a few basic equations:
1) Based on the mass of the car, the radius of the turn, and the speed around the turn, you should be able to calculate the centripedal force.
2) Since static friction is based on the normal force and the coefficient of static friction, you should be able to calculate that coefficient given the centripedal force.
OK, great...now that we have that coefficient, we're set for the second part. Why does a banked turn help a car maintain a greater speed? In the flat case, the only centipedal force is applied because of static friction. However, in a banked turn, there are
two forces which help with the turn: static friction, and the component of the normal force which points towards the center of the turn.
The key to this part of the problem will be to draw the vector decomposition diagram in the right way. In order for the car to move through the turn, you have to balance the forces along each axis. To maintain circular motion at the new speed, you have to sum the force components in the centripedal direction from static friction and the normal force. Along the ramp, though, you also have to balance some forces since the component of static friction along the ramp must be enough to keep the car from slipping down the ramp under its own weight. The force components in each direction will be a function of the bank angle, but since you solved part 1 of the problem, you should know all of the other values. Solve for the bank angle, and you're in business.
Hope this helps...