Meet Up Catch-Up Problem Combination: Problem 2

Problem: Cars Alpha and Beta begin from points A and B, starting towards each other at the same time. Right after arriving at one point, the two cars turn around. It is given that the speed of Car Alpha is 3/7 that of Car Beta's. On their 2007th time meeting (this counts both catching up and meeting) and their 2008th time meeting spots are 120 kilometers away from each other. What is the length between A and B?

Key: Find a pattern

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