Maths Olympiad Prep

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Geometry Difficulty 5.3 AIME, harder Find the answer

55. Xiao Ming, Xiao Qiang, and Xiao Hong are playing hide-and-seek together. Xiao Ming says to Xiao Qiang: “I am 5 meters directly north of you”; Xiao Hong says to Xiao Qiang: “I am 6 meters directly south of you”. If Xiao Qiang needs 6 steps to walk 1 meter, how many steps does he need to walk in total to catch Xiao Ming first and then Xiao Hong?

A number or a short expression. Spacing and $ signs are ignored.

Solution

Reference answer: 96

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.