A manufacturer builds 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 = ?

A. $$8 - x = 2$$

B. $$\frac{1}{8} + \frac{1}{x} = \frac{1}{2}$$

C. $$\frac{{500}}{8} + \frac{{500}}{x} = 500$$

D. $$\frac{x}{2} + \frac{x}{8} = 1$$

Answer: Option B

Solution(By Examveda Team)

Number of envelopes addressed by first machine in 1 minute
$$ = \frac{{500}}{8}$$
Number of envelopes addressed by second machine in 1 minute
$$ = \frac{{500}}{x}$$
Number of envelopes addressed by both machine in 1 minute
$$\eqalign{ & {\text{ = }}\frac{{500}}{2} \cr & \therefore \frac{{500}}{8} + \frac{{500}}{x} = \frac{{500}}{2} \cr & \Rightarrow \frac{1}{8} + \frac{1}{x} = \frac{1}{2} \cr} $$