Good morning, Marius
Try to use the Space Time axes George (x,t) and Gracie (x’,t’) or in other words, World Lines (t,t’) and Now Lines (x,x’). I find much better understanding using them.
For better explanation, while George remains at the Start line, he has a friend (Peter) at the Finish Line. Both of them have clocks in sync.
When Gracie’s World Line (x’=0) crosses the Peter’s World Line (x=156 lt.min), the Now Line of Gracie is (t’=65 min) and the Now Line of Peter and George is (t=169min).
The “Problem” starts when Gracie makes numbers, without using the Space Time diagram:
The Now Line of Gracie (t’=65 min) crosses the World Line of George (x=0) at (t=25 min). Thinking twice now, she sees her Now Line (t’=0) while crossing the George’s World Line (x=0) at (t=0), crosses the Peter’s World Line (x=156lt.min) at (t=144 min) and solve the problem making 25+144 =169 min!
But if she were using the Space Time diagram, she would see that her Now Line (t’=65min) also crosses the World Line of Peter (x=156 lt.min) at (t = 169 min)

Thank you very much Marius, now I realize that data of 100ns of Train’s front clock refers to the coordinate (Δt’), while I was mistakenly confusing with (Δt). Now Professor Brian explanation is clear to me!

My comment refers to 22.11, where Professor Brian wrote 100ns = (v)(L0/2)/c^2.
Following 8.1 it should be 100ns = (v) (L/2)/(c^2-v^2), and with 200ns = L/v,
results in v = 0.7c; γ = 1.41; L = 141’ and L0 = 200’

Great Course, Professor Green! I started browsing through the animation pictures of your Light Clock, then watching the Characters George and Gracie and every time I was feeling more enthusiast while jumping from Modules at the middle to Modules at the end.
Now, revisiting the Course in a quieter mood I found myself deeply impressed with your way of teaching. Yes, dropping and practising with the addition velocity formula is the best way of awake our feelings accustomed to Newtonian Mechanics.