National problem · Geometry

Metka is standing \(60\) m east and \(80\) m south of the spot where Tine is standing. Both are the same distance from a linden tree in the town park, and the tree stands due east of Tine's spot. At the same moment each of them sets off from their own spot and walks straight towards the tree. How many metres does each of them walk before they meet under the tree?

East is to the right, south is downward. Tine stands at \(T\), Metka at \(M\), the linden at \(L\); distances in metres.

Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2003, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source

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