1962 AHSME Problem 35

A man on his way to dinner shortly after 6: 00 p.m. observes that the hands of his watch form an angle of 110^{\circ}. Returning before 7: 00 p.m. he notices that again the hands of his watch form an angle of 110^{\circ}. The number of minutes that he has been away is:

\textbf{(A)}\ 36 \frac23 \qquad \textbf{(B)}\ 40 \qquad \textbf{(C)}\ 42 \qquad \textbf{(D)}\ 42.4 \qquad \textbf{(E)}\ 45

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