KöMaL 2016 K490

Anthony is training ants. The performance starts with 99 ants sleeping on a 1-metre long straight rod. When a whistle is blown, they all wake up at the same time, and start crawling towards an end of the rod, at a speed of 1 cm/s. If an ant reaches the end of the rod, it will leave the rod. If two ants meet, they will turn back immediately, and start crawling in the opposite direction. The performance ends when the last ant has left the rod. What is the maximum possible duration of the performance?