AHSME 1950 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: $\textbf{(A)}\ 8-x=2 \textbf{(B)}\ \dfrac{1}{8}+\dfrac{1}{x}=\dfrac{1}{2} \textbf{(C)}\ \dfrac{500}{8}+\dfrac{500}{x}=500 \textbf{(D)}\ \dfrac{x}{2}+\dfrac{x}{8}=1 \\ \textbf{(E)}\ \text{None of these answers}$