I agree, this is not an optimization problem. EDIT: Well, I guess you could consider the task to be optimizing the distance Agatha can travel first class.
I'll get you started, though:
Let $\displaystyle A = $ distance, in km, traveled first class.
Let $\displaystyle B = $ distance, in km, traveled second class.
Your two equations are:
$\displaystyle .40A + .10B = 465$
$\displaystyle A + B = 1500$
Now, how can you relate these two equations to each other?
$\displaystyle 0.4x+0.1y=465$ and $\displaystyle x+y=1500$ then i solved for y in the first equation and got $\displaystyle y=4650-4x$ which I then plugged in to the second forumla and solved for x=1050, which, I think, is the number of kilometers the traveller would ride first class, is that right?