AHSME 1962 Problem 13

$R$ varies directly as $S$ and inversely as $T$. When $R = \frac{4}{3}$ and $T = \frac {9}{14}$, $S = \frac37$. Find $S$ when $R = \sqrt {48}$ and $T = \sqrt {75}$. $\textbf{(A)}\ 28 \textbf{(B)}\ 30 \textbf{(C)}\ 40 \textbf{(D)}\ 42 \textbf{(E)}\ 60$