Here is my problem:

If Sara is twice as old as Eileen will be when Gina is as old as Sara is now, who is the oldest, the middle child, and the youngest?

I have deduced that, obviously, Eileen is not the oldest. She is, at some point, half the age of Sara. Gina also cannot be the oldest because of how it is worded: "as old as Eileen WILL BE WHEN Gina is as old as Sara is NOW." So Sara has to be the oldest, right?

I cannot figure out how to determine who is the middle child and who is the youngest.

We know that S = 2E when G = S... So G = 2E at some point too, right?

That makes Gina the middle child, and Eileen the youngest. Do I have this right?