Existence, Uniqueness & Bifurcations · Superchallenge problem

A logistic population (as a fraction of carrying capacity) with constant harvesting obeys $y' = y(1 - y) - h$. The harvest is set just past the collapse threshold, at $h = \dfrac14 + \dfrac{1}{100}$. Starting from $y(0) = 1$, how long does it take the population to reach $0$?