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\frac{\pi}{12}t - \phi = 0 \Rightarrow t = \frac{12}{\pi} \cdot \phi \approx \frac{12}{\pi} \cdot 1.176 \approx 4.49 \text{ hours}
So the maximum value of $ f(t) $ is $ \boxed{13} $, and it occurs at approximately $ \boxed{4.49} $ hours after midnight, or around 4:29 AM.
Question: A city planner is designing a periodic stormwater drainage system that follows a sinusoidal pattern over the year. The water level is modeled by $ w(t) = 7\sin\left(\frac{\pi}{6}t\right) + 24\cos\left(\frac{\pi}{6}t\right) $, where $ t $ is in months. What is the maximum water level, and when does it first occur?

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