Urgently needing the cash prize, Lou enters the Rest-to-Rest auto competition, in which each contestant's car begins and ends at rest, covering a distance L in as short a time as possible. The intention is to demonstrate mechanical and driving skills, and to consume the largest amount of fossil fuels in the shortest time possible. The course is designed so that maximum speeds of the cars are never reached. If Lou's car has a maximum acceleration of a, and a maximum deceleration of 2a, then at what fraction of L should Lou move his foot from the gas pedal to the brake? What fraction of the time for the trip has elapsed at that point?