part (i) is basically solving system of linear equations.

substitute 3 known points ...
1. highest point of tunnel
2. width of track bed
3. upper corner of train with goods
... to get 3 equations.

part (ii) can be solved by algebraic method or by rearranging to get standard equation of ellipse.

P.S.
have you got solution for your breakfast food consumer problem which you posted earlier?
That is also a problem involving system of linear equations. If you still need, you can repost it again and i will submit answer for you. (The market shares for x,y and z are 4/15, 1/15 and 2/3.)