anonymous 5 years ago a train leaves the station at 10am and travels due south at a speed of 60km/h. Another train has been heading due west at 45km/h and reaches the same station at 11am. At what time were the two trains closest together. what would the diagram look like?

That depends highly on the lattitude of the station. Because if you go back far enough the two trains were both at the station and then the second train went one time all around the earth in direction west. But if the station is near one of the poles, that time is not that long ago, while if the station is at the equator, it is before $\frac{40000\; km }{45\; km\;/\;h} \approx 889\; h = 37\; \text{days}\; 1\;h$