Ruby: How to calculate a path relative to another one?

Let's say I know the absolute path that I am starting from and the absolute path that I am trying to get to:

first = '/first/path'
second = '/second/path'

Now I want to figure out how to construct a path that is relative to the first. For example:

# answer should be /first/path/../../second/path
path = second.get_path_relative_to(first)

How can I do this sort of thing in Ruby?