Btw, shouldn't your 2nd solution be 50, not 54?
Yes, I misread my own scribble. Also, I didn't explain that the point Y is the position of Y when X is back at A.
I'm curious about this 2nd solution: obviously to be rejected, since BC = 65.
However, can it be made to work, like with Y going in reverse for a while?!
Any thoughts on that? Thanks.
It implies YD and AC are negative distances, and the question requires X and Y to be travelling towards each other; if they are heading in the same direction, then C is outside AB, but then AD cannot be less than BC.
If you assume that Y changes direction the moment X arrives back at A, then you get 24*65 = (2BC+AD-AB)(AB-BC) = (154-AB)(AB-65), which makes AB = 89 or 130. To flip the other factor you need AB<BC and it's too big a change to the question.