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jmc

prealgebra senior

Problem

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?
Solution
To make the distance between exit and exit as long as possible, we want to make the distance between any other two consecutive exits as short as possible (that is, km). There are nine distances between exits from exit to exit ; eight that we want to make as short as possible and one that we want to make as long as possible. Thus, the longest possible distance is km.
Final answer
52