Random Ants on a String

500 ants are randomly placed on a 1-foot string (each ant's position is independent and uniformly distributed between 0 and 1). Each ant independently and randomly chooses a direction (left or right with equal probability) and moves at a constant speed of 1 foot per minute. When two ants collide head-on, they both immediately reverse direction and keep moving at 1 foot per minute. An ant falls off the string when it reaches either end. Assume the ants are infinitely small.

Question: What is the expected time for all ants to fall off the string?