Five hundred bouncing ants on a one-foot string

A string is one foot long. Five hundred ants are dropped onto it at independent uniformly random positions, each facing left or right at random, and all crawl at one foot per minute. Whenever two ants meet they both turn around. An ant reaching an end falls off. What is the expected time until the string is empty?

$\tfrac{500}{501}$ minutes. A collision with reversal looks exactly like the two ants passing through each other, so the string empties when the slowest 'ghost' ant walks off. Each ghost's exit time is the distance to the end it faces, which is uniform on $[0,1]$, and the expected maximum of $500$ such uniforms is $\tfrac{500}{501}$.