Here is the derivation of my equation:



For identical speeds, the wolf can not only never catch the chicken, but it should also never be exactly on the same x-coordinate as the chicken! It will get arbitrarily close to x = d though, but never reach it. At least that is what I think.

So it doesn't make sense for me to have the speed be a factor in the asymptote. I think it should always be at x = d, if the speeds are identical.