Problem 3 (2012 AMC 8)

On February $13$ The Oshkosh Northwester listed the length of daylight as $10$ hours and $24$ minutes, the sunrise was $6\text{:}57\text{AM}$, and the sunset as $8\text{:}15\text{PM}$. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?