1. **State the problem:** We have a stamping machine that can stamp 40 envelopes in 8 minutes. We want to find how many such machines working simultaneously are needed to stamp 120 envelopes per minute. 2. **Find the rate of one machine:** The rate of one machine is $$\frac{40 \text{ envelopes}}{8 \text{ minutes}} = 5 \text{ envelopes per minute}.$$ 3. **Determine the total rate needed:** We want to stamp 120 envelopes per minute. 4. **Calculate the number of machines required:** Let the number of machines be $n$. Since each machine stamps 5 envelopes per minute, together they stamp $5n$ envelopes per minute. We set up the equation: $$5n = 120$$ 5. **Solve for $n$:** $$n = \frac{120}{5} = 24.$$ 6. **Conclusion:** 24 stamping machines working at the same time are required to stamp 120 envelopes per minute.