1962 AHSME Problem 24

Three machines \text{P, Q, and R,} working together, can do a job in x hours. When working alone, \text{P} needs an additional 6 hours to do the job; \text{Q}, one additional hour; and R, x additional hours. The value of x is:

\textbf{(A)}\ \frac23 \qquad \textbf{(B)}\ \frac{11}{12} \qquad \textbf{(C)}\ \frac32 \qquad \textbf{(D)}\ 2\qquad \textbf{(E)}\ 3

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