Second-lap speed for a 60 mph average

You drive one lap of a one-mile track at $30$ mph. How fast must you drive a second one-mile lap so that your average over both laps is $60$ mph?

It is impossible. A $60$ mph average over $2$ miles allows $2$ minutes in total, but the first lap at $30$ mph already used $2$ minutes. No finite speed on the second lap works.