Have you been on a moving sidewalk, or they are sometimes called people movers. You find them at many airports. It is a large belt of plastic or rubber at the floor level, about a wide as a sidewalk and about half a block long. The belt moves slowly and if you stand on it you move the half a block with no effort on your part.
Imagine that there is a very long moving sidewalk that moves at 100 km/hr. Someone gets on it and then you get on 15 minutes later. The person ahead of you has progressed at 100 km/hr for 1/4 of an hour and hence he is 25 km ahead of you. If both of you stand still you remain 25 km apart even though you are both moving at 100 km/hr. Now you start to walk at 20 km/hr. At this speed it takes you one and a quarter hours to move the 25 km that separate you.
From your point of view, on the moving sidewalk, you traveled at 20 km/hr for an hour and a half to catch the other person. From the point of view of someone not on the moving sidewalk, the first person traveled at 100 km/hr, you traveled at 120 km/hr, and it took you one and a quarter hours to catch up.
I hope this helps,