Question

A manufacturer built a machine which will address 500 envelops in 8 minutes. He wishes to build another machine so that when both are operating together they will address 500 envelops in 2 minutes. The equation used to find how many minutes x it would require the second machine 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. $\frac{x}{2}+\frac{x}{8}=1$
• E. None of these

Answer 1

The correct option is B $\frac{1}{8}+\frac{1}{x}=\frac{1}{2}$

Since the first machine addresses 500 envelopes in 8 minutes, it addresses 500/s envelopes in 1 minute and 2. 500/8 in 2 minutes. If the second machine addresses 500 envelopes in x minutes, then it addresses. 500/envelopes in 2 minutes. To determine x so that both machines together address 500 envelopes in 2 minutes we use the condition
$500\frac{2}{x}.500=500$ or $\frac{500}{8}+\frac{500}{x}=250$
or $\frac{1}{8}+\frac{1}{x}=\frac{1}{2}$