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tortoise and lizard walk around a rectangle

Source: I May Olympiad (Olimpiada de Mayo) 1995 L1 P5

September 17, 2022
geometryalgebrarectangle

Problem Statement

A tortoise walks 6060 meters per hour and a lizard walks at 240240 meters per hour. There is a rectangle ABCDABCD where AB=60AB =60 and AD=120AD =120. Both start from the vertex AA and in the same direction (A→B→D→AA \to B \to D \to A), crossing the edge of the rectangle. The lizard has the habit of advancing two consecutive sides of the rectangle, turning to go back one, turning to go forward two, turning to go back one and so on. How many times and in what places do the tortoise and the lizard meet when the tortoise completes its third turn?
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