1950 AHSME Problem 50

A privateer discovers a merchantman 10 miles to leeward at 11\text{:}45 \text{ a.m.} and with a good breeze bears down upon her at 11 mph, while the merchantman can only make 8 mph in his attempt to escape. After a two hour chase, the top sail of the privateer is carried away; she can now make only 17 miles while the merchantman makes 15. The privateer will overtake the merchantman at:

\textbf{(A)}\ 3\text{:}45\text{ p.m.}\qquad\textbf{(B)}\ 3\text{:}30\text{ p.m.}\qquad\textbf{(C)}\ 5\text{:}00\text{ p.m.}\qquad\textbf{(D)}\ 2\text{:}45\text{ p.m.}\qquad\textbf{(E)}\ 5\text{:}30\text{ p.m.}

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