A tree, left undisturbed, will go on to live for hundreds of years. So, a tree being relatively elderly does not reduce its remaining life. The medical researcher, on the other hand, has gone through approximately 2/3 of his life. Thinking in terms of person-years saved, it might make sense to save the baby instead. Of course, this is ignoring the aggregate benefit to society the researcher might provide over his remaining years. So it's only utilitarian on an individual level instead of an aggregate level, but it's a utilitarian justification nevertheless.

But then this could just be me trying to retrospectively justify my inclination to save the baby.