1. **State the problem:** Mr. Wells has two copiers. The first copier makes 1,000 copies in 30 minutes, and the second copier makes 1,000 copies in 20 minutes. We want to find how long it takes both copiers working together to make 1,000 copies. 2. **Formula and concept:** When two machines work together, their rates add up. The rate is copies per minute. Rate of first copier = $\frac{1000}{30} = \frac{100}{3}$ copies per minute. Rate of second copier = $\frac{1000}{20} = 50$ copies per minute. Combined rate = rate1 + rate2. 3. **Calculate combined rate:** $$\text{Combined rate} = \frac{100}{3} + 50 = \frac{100}{3} + \frac{150}{3} = \frac{250}{3}$$ copies per minute. 4. **Find time to make 1,000 copies together:** Time = $\frac{\text{Total copies}}{\text{Combined rate}} = \frac{1000}{\frac{250}{3}}$ 5. **Simplify the time:** $$\frac{1000}{\frac{250}{3}} = 1000 \times \frac{3}{250} = \frac{3000}{250}$$ 6. **Simplify the fraction:** $$\frac{3000}{250} = \frac{\cancel{3000}^{12}}{\cancel{250}^{10}} = 12 \text{ minutes}$$ **Final answer:** It will take the two copiers working together 12 minutes to make 1,000 copies.