An Amphibious Car Would Be So Useful In This Problem.

Calculus Level 4

Benito the Bandit is hiding out in the center of a large circular lake of radius \( 30 \) miles. He has access to a speedboat, which can travel at a maximum speed of \( 30 \) miles per hour.

Police officer Parker arrived in his Chevrolet Impala police cruiser, with a court order to capture Benito the Bandit. He is a single officer, and is unable to drive (or swim, or fly) over the lake. He figures that the best way to capture Benito is to always drive towards the point on the shore which is closest to Benito.

What is the minimum integer speed at which Officer Parker would have to be able to drive, in order to be certain of catching Benito right when Benito reaches the shore?

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