1. **State the problem:** Jack can carry a pail of water uphill alone in 40 minutes, Jill can do it alone in 25 minutes, and we want to find how long it takes if they help each other carrying the pail. 2. **Define work rates:** Jack's work rate is $\frac{1}{40}$ (portion of the hill per minute). 3. Jill's work rate is $\frac{1}{25}$ (portion of the hill per minute). 4. **Combined work rate:** When working together, their rates add: $$ \frac{1}{40} + \frac{1}{25} = \frac{25}{1000} + \frac{40}{1000} = \frac{65}{1000} = \frac{13}{200} $$ 5. **Calculate combined time:** The time taken working together is the reciprocal of their combined rate: $$ t = \frac{1}{\frac{13}{200}} = \frac{200}{13} \approx 15.38 \text{ minutes} $$ 6. **Conclusion:** Together, Jack and Jill can carry the pail uphill in approximately 15.38 minutes.