AHSME 1962 Problem 35

A man on his way to dinner short 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: $\textbf{(A)}\ 36\frac{2}3 \textbf{(B)}\ 40 \textbf{(C)}\ 42 \textbf{(D)}\ 42.4 \textbf{(E)}\ 45$