Algebra · Ratio and proportion · Uniform motion · Least common multiple
Ana and Beno cycle clockwise along the rectangular track shown in the figure, on which the length of every section is marked. Ana rides the shorter of the two loops, Beno the longer one, and their speeds are in the ratio \(v_{\text{Ana}} : v_{\text{Beno}} = 2 : 7\). Both set off at the same moment from the point \(S\). How many laps will Ana have ridden, and how many Beno, when the two of them are for the first time again at the point \(S\) together?
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), regijsko (regional) round 2014, 1. letnik, category A, problem B3. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source