Romeo and Juliet

Calculus Level 4

Romeo lives on the shore of a circular lake of radius \(1\text{ km}\) and Juliet also lives on the shore but diametrically opposite of Romeo's house. Romeo always goes to Juliet's house every day and secretly meets her. He rows a boat at \(3\text{ km/h}\) and walks at \(6\text{ km/h}\) in order to meet Juliet.

If he always moves towards Juliet, then the longest possible time in minute to get Juliet's house can be expressed as \(\text{T}\). Determine the value of \(\lfloor \text{T}\rceil\).

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