Answered! A 10-foot rope is stretched horizontally across a gap. n ants are distributed on top of the rope, each facing along the…

A 10-foot rope is stretched horizontally across a gap. n ants are distributed on top of the rope, each facing along the rope in one of the two possible directions. At the same instant, the ants begin to walk (crawl?) at a rate of 10 feet per minute. If two ants collide, they immediately reverse direction. When an ant reaches the end of the rope, it steps off the rope and can non longer block the other ants. (a) What is the largest possible amount of time that can elapse before the last ant steps off the rope (in terms of n the number of ants on the rope initially)? (b) What initial configuration of ants gives this worse-case time?