Models & Qualitative Behavior · Superchallenge problem

Water is poured at a constant rate into an initially empty tank that also leaks through a hole in its base. The depth $h$ (in metres) satisfies $h' = 1 - \sqrt{h}$ ($t$ in hours), so the depth approaches $1$ m. How many hours does it take to reach a depth of $\dfrac{9}{16}$ m? Give an exact answer.