Romeo and Juliet

Calculus Level 5

Romeo lives on the shore of a circular lake of radius 1 km1\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 km/h3\text{ km/h} and walks at 6 km/h6\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 T\text{T}. Determine the value of T\lfloor \text{T}\rceil.

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