Random ants

$500$ ants are placed on a $1$-foot string without any order. Assume independent uniform distribution for each ant. Each ant will move randomly towards either end of the string at a constant speed of $1$ foot per minute. The ants will keep moving until they reach the end of the string, and if two ants collide head-on, they will both immediately turn around and continue moving. Assuming that the size of the ants is infinitely small, what is the expected time for all $500$ ants to fall off the string?