AHSME 1952 Problem 32

$K$ takes $30$ minutes less time than $M$ to travel a distance of $30$ miles. $K$ travels $\frac {1}{3}$ mile per hour faster than $M$. If $x$ is $K$'s rate of speed in miles per hours, then $K$'s time for the distance is: $\textbf{(A)}\ \dfrac{x + \frac {1}{3}}{30} \textbf{(B)}\ \dfrac{x - \frac {1}{3}}{30} \textbf{(C)}\ \frac{30}{x+\frac{1}{3}} \textbf{(D)}\ \frac{30}{x} \textbf{(E)}\ \frac{x}{30}$