2012 AMC 8 Problem 3

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

\textbf{(A)}\ 5:10\text{pm}\quad\textbf{(B)}\ 5:21\text{pm}\quad\textbf{(C)}\ 5:41\text{pm}\quad\textbf{(D)}\ 5:57\text{pm}\quad\textbf{(E)}\ 6:03\text{pm}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.