Final answer:
The distance between the 5-car and 8-car stop markers is 3 car lengths, which accounts for the difference in length of the two trains and ensures that each train, when properly stopped, is centered in the station.
Step-by-step explanation:
The question is asking how far apart the 5-car and 8-car stop markers are, assuming that trains of different lengths are centered when they stop at the station. To answer this, we must consider the train stop markers as points along a line where the middle of the train should stop.
If a train is centered at each marker, it means that half of the train extends in one direction from the marker, and the other half extends in the opposite direction. When a 5-car train is at its marker, 2.5 car lengths will extend on either side. For an 8-car train, 4 car lengths will extend on either side of its marker. Thus, the difference in the extent on one side between the 5-car and 8-car stop markers will be 4 car lengths minus 2.5 car lengths, which is 1.5 car lengths.
To find the total distance between the 5-car and 8-car markers, we have to double that amount because the train extends on both sides of the marker. Therefore, the distance between the 5-car and 8-car stop markers must be 3 car lengths.