smc

We first represent the first machine's speed in per $2$ minutes: $125\text{ envelopes in }2\text{ minutes}$. Now, we know that the speed per $2$ minutes of the second machine is $$500-125=375\text{ envelopes in }2\text{ minutes}$$ Now we can set up a proportion to find out how many minutes it takes for the second machine to address $500$ papers: $\frac{375}{2}=\frac{500}{x}$. Solving for $x$, we get $x=\frac{8}{3}$ minutes. Now that we know the speed of the second machine, we can just plug it in each option to see if it equates. We see that $\boxed{\frac{1}{8}+\frac{1}{x}=\frac{1}{2}}$ works.