We have a train that is 400 meters long in its reference frame and a tunnel that is 380 meters long it its own reference frame. The train travels through the tunnel at great speed. According to the conductor on the train, it would be possible for the train to fit completely in the tunnel.

ok so what I think is that if the correction factor is less than one then this wouldn't be possible but my problem is that I have trouble figuring out which is the proper and which is the observer time, and that makes a big difference lol.

so first, let me know if I had the correct way to look at this problem, and second, please explain in an intuitive way how I can distinguish between proper and observer time, like for example if the question ask "in the platform's reference frame." How would I understand what is asking for?