# Romeo and Juliet

Calculus Level 5

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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