1. **Problem:** Clayton can sweep the gym floor in 24 minutes, and Morgan can do it in 40 minutes. How long will it take if they work together? 2. **Formula:** When two people work together, their combined work rate is the sum of their individual rates. The time taken together is given by: $$\text{Time together} = \frac{1}{\frac{1}{t_1} + \frac{1}{t_2}}$$ where $t_1$ and $t_2$ are the times taken individually. 3. **Calculate individual rates:** Clayton's rate = $\frac{1}{24}$ floor per minute. Morgan's rate = $\frac{1}{40}$ floor per minute. 4. **Sum of rates:** $$\frac{1}{24} + \frac{1}{40} = \frac{5}{120} + \frac{3}{120} = \frac{8}{120} = \frac{2}{30}$$ 5. **Time together:** $$\text{Time} = \frac{1}{\frac{2}{30}} = \frac{1}{\cancel{\frac{2}{30}}} = \frac{30}{2} = 15 \text{ minutes}$$ **Answer:** It will take them 15 minutes to sweep the floor together.