As a warm-up, Gene is trying to do everyone’s favorite Pacer Test, which involves running back and forth between two markers 20 m apart in a sufficient amount of time. When Gene runs, he starts from rest, accelerates at a constant rate, decelerates at a constant rate, and finishes at rest in order to make the next lap as soon as possible. The Pacer test starts slow, but picks up speed for each lap. Gene is on one of the last laps and is starting to lose breath already. If Gene can accelerate at 0.3 m/s^2 and decelerate at 1.2 m/s^2, how long is the fastest 20 m lap he could possibly run?

As a warm-up, Gene is trying to do everyone’s favorite Pacer Test, which involves running back and forth between two markers 20 m apart in a sufficient amount of time. When Gene runs, he starts from rest, accelerates at a constant rate, decelerates at a constant rate, and finishes at rest in order to make the next lap as soon as possible. The Pacer test starts slow, but picks up speed for each lap. Gene is on one of the last laps and is starting to lose breath already. If Gene can accelerate at 0.3 m/s^2 and decelerate at 1.2 m/s^2, how long is the fastest 20 m lap he could possibly run?