Exits on a highway are numbered consecutively from 1 to 50. The distance from exit 41 to exit 50 is 100 km. If each exit is at least 6 km from the next exit, what is the longest possible distance, in kilometers, between exit 47 and exit 48?
I need to find the maximum distance between two consecutive exits, so I want to minimize the distances between the other exits. The problem says that each exit is at least 6 km from the next one, so I can assume that the distance between any two exits that are not 47 and 48 is 6 km. Similarly, the distance from exit 49 to exit 50 is 6 km. Now, I want to maximize the distance from exit 47 to exit 48, so I want to minimize the distance from exit 46 to exit 47 and the distance from exit 48 to exit 49. Again, I can assume that these distances are 6 km each, since that is the minimum possible. So, the distance from exit 47 to exit 48 is 64 - 6 - 6 = 52 km. This is the longest possible distance between these two exits. 