Hello, Before anyone thinks this is a coursework question, it is not. It is a challenge problem, which I found online, and seems worth discussing. (Question) In a 400-m relay race the anchorman (the person who runs the last 100 m) for team A can run 100 m in 9.8 s. His rival, the anchorman for team B, can cover 100 m in 10.1 s. What is the largest lead the team B runner can have when the team A runner starts the final leg of the race, in order that the team A runner not lose the race? The answer is 3.0m, how? Calculus please (wherever applicable). First we have team A, which we can denote by [itex]A[/itex] <--- The anchorman Team B can be denoted by [itex]B[/itex] <-- The anchorman Since [itex]v_a(t) = 10.204 m/s[/itex] [itex]v_b(t) = 9.9009 m/s[/itex] [itex]x_a(t) = 10.204t[/itex] [itex]x_b(t) = 9.9009t[/itex] But [itex]x_a(t) > x_b(t)[/itex] for all real [itex]t[/itex] so, runner B cant overtake runner A?