The only principle missing is that if you are moving away from a source of light, then you are running away from the light, and so it has to travel more to catch up to you.
Think of two runners: A is at position 0, and B is 500 meters ahead. B is not as fast as A, so eventually A will catch up to B. However, by the time this happens, B will be further along, so A will have traveled more than 500 meters. This will take more than 50 seconds if A is only going 10 meters per second.
The only way this analogy is deceptive is that galaxies are moving apart mostly because the space in between is expanding. So A, the light from a galaxy, is going at a fixed speed; B, which represents us the observers, is standing still; and the track itself is stretching everywhere.
In fact, putting in some rough numbers with my smart phone app of all things, galaxies at a redshift of 10 emitted the light we see at 490 million years post-Big Bang, some 13.4 billion years ago. The universe was 9.1% its current linear size back then, so that gives you some idea about how fast the track has expanded.