AHSME 1950 Problem 50

A privateer discovers a merchantman $10$ miles to leeward at 11:45 a.m. and with a good breeze bears down upon her at $11$ mph, while the merchantman can only make $8$ mph in her 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: $\textbf{(A)}\ 3\text{:}45\text{ p.m.} \textbf{(B)}\ 3\text{:}30\text{ p.m.} \textbf{(C)}\ 5\text{:}00\text{ p.m.} \textbf{(D)}\ 2\text{:}45\text{ p.m.} \textbf{(E)}\ 5\text{:}30\text{ p.m.}$