1973 AHSME Problem 27

Cars A and B travel the same distance. Care A travels half that distance at u miles per hour and half at v miles per hour. Car B travels half the time at u miles per hour and half at v miles per hour. The average speed of Car A is x miles per hour and that of Car B is y miles per hour. Then we always have

\textbf{(A)}\ x \leq y\qquad \textbf{(B)}\ x \geq y \qquad \textbf{(C)}\ x=y \qquad \textbf{(D)}\ x<y\qquad \textbf{(E)}\ x>y

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