1. **State the problem:** If 7 machines take 7 minutes to produce 7 widgets, how many minutes will it take 35 machines to produce 35 widgets? 2. **Understand the rate:** 7 machines produce 7 widgets in 7 minutes. This means 1 machine produces 1 widget in 7 minutes because the work is evenly distributed. 3. **Formula:** Time = \frac{Number\ of\ widgets}{(Machines \times Rate\ per\ machine)} 4. Since 1 machine produces 1 widget in 7 minutes, the rate per machine is \frac{1\ widget}{7\ minutes}. 5. For 35 machines producing 35 widgets, the time taken is: $$\text{Time} = \frac{35\ widgets}{35\ machines \times \frac{1\ widget}{7\ minutes}}$$ 6. Simplify the denominator: $$35 \times \frac{1}{7} = 5$$ 7. So, $$\text{Time} = \frac{35}{5} = 7\ minutes$$ **Final answer:** It will take 35 machines 7 minutes to produce 35 widgets.