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The depth of water in a harbor is modeled by the function d(t) = 5 * cos(πt/6) + 7, where d(t) is the depth in meters and t is the time in hours since midnight. If a boat requires at least 6 meters of water to dock, by what time must it leave the harbor? When can it return? Give the answers in HH:MM to the nearest minute.

Explore how to use trigonometric functions to model the depth of water in a harbor and determine the time when a boat can dock or return. This problem involves solving a cosine equation for specific times, suitable for students in Grades 10-12.

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