AHSME 1973 Problem 20

A cowboy is 4 miles south of a stream which flows due east. He is also 8 miles west and 7 miles north of his cabin. He wishes to water his horse at the stream and return home. The shortest distance (in miles) he can travel and accomplish this is $\textbf{(A)}\ 4+\sqrt{185} \textbf{(B)}\ 16 \textbf{(C)}\ 17 \textbf{(D)}\ 18 \textbf{(E)}\ \sqrt{32}+\sqrt{137}$