Mathematics

Mathematics

Problem

In a 400 m400\,\text{m} race on a track with semicircular ends of radius 35 m35\,\text{m}, the inner lane (Lane 1) has a total length of exactly 400 m400\,\text{m} along its inner edge. Lane 2 is 1.2 m1.2\,\text{m} wide and is immediately outside Lane 1. How far ahead of the Lane 1 start line must the Lane 2 runner start to run the same distance, assuming they run 20 cm20\,\text{cm} from the inner edge of their respective lanes?

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