Time and space are intimately locked together into what Einstein called "space-time". The distance one has yet to travel during a trip increasingly contracts with increasing speed. This is entirely apart from the obvious shortening due to their having already traveled some of the distance.
...to put it another way, a moving clock ticks out time more slowly than a stationary one at your side. In fact, it has been experimentally verified that people aboard fast-moving air or space craft actually experience a shorter length of time than the counterparts on the ground. In other words, to a very minute degree, they’ve actually moved ahead in time, vs earthbound folks. They used an atomic clock to measure.
But that example deals entirely with SPACE, not time.