Time Span and Date Time Computation

Oh, great.
This is not about programming but about elementary mathematics (well, very elementary).

This problem is ill-posed. You cannot calculate this time, because the route and schedule is not provided. In other words, you need a detailed trajectory of the train in the space-time (called World line) and information about sunset/sunrise for every point in space (not just for each city). Also, this, strictly speaking, depends on how you define sunset/sunrise: it can be a local time in trajectory point or official value for the time zone, which is slightly different. Also, you should take into account, that sunset/sunrise changes as the train goes.

I can explain why you cannot solve this problem without this additional information.

To illustrate this, let's consider two different schedules. Consider the train move in a straight line. In one case, train moves exactly half of the way at very slow speed, the rest of the way at fast speed. In second case is just the opposite: fast, then slow, to take the same time for the whole travel. As the train moves East to West and departs before sunset, it meets sunset at some point which happens sooner for second case. Draw three World lines on a 2D picture (abscissa: time, ordinate: longitude, two lines for two train schedules and third line for sunset points), show intersections of the train lines with the sunset line and you will see it.

Please don't tell me now it is that the train moves at constant speed along straight trajectory or other assumptions. 1) In real life this is not the case; 2) even if you want to solve very idealized problem, none of the idealization are assumed, but should be specified precisely.

The problem is finalized: there is no unambiguous solution.