1950 AHSME Problem 29

A manufacturer built a machine which will address 500 envelopes in 8 minutes. He wishes to build another machine so that when both are operating together they will address 500 envelopes in 2 minutes. The equation used to find how many minutes x it would require the second machine to address 500 envelopes alone is:

\begin{array}{l} \textbf{(A)}\ 8-x=2\qquad\textbf{(B)}\ \frac{1}{8}+\frac{1}{x}=\frac{1}{2}\qquad\textbf{(C)}\ \frac{500}{8}+\frac{500}{x}=500\qquad\textbf{(D)}\ \frac{x}{2}+\frac{x}{8}=1\qquad\\ \textbf{(E)}\ \text{None of these answers} \end{array}

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