This was given as a problem in a calculus textbook I'm working through (apologies if this should have gone in the physics forum) 1. The problem statement, all variables and given/known data An ant crawls at 1foot/second along a rubber band whose original length is 2 feet. The band is being stretched at 1 foot/second by pulling the other end. At what time T, if ever, does the ant reach the other end? One approach: The band's length at time t is t + 2. Let y(t) be the fraction of that length which the ant has covered, and explain (a) y' = 1/(t + 2) (b)y =ln(t + 2) -ln 2 (c) T = 2e -2. 2. Relevant equations ∫1/x dx = ln(x) 3. The attempt at a solution Given a, I can get to b by integrating and finding the constant, and then to c by solving for y=1, but I'm stumped on how to get to explain a. y' seems to be the ant's speed over the length of the band, by I don't understand why that is so.