1. **Problem 1: Find the mean, median, and mode of the numbers:** 17, 18, 16, 17, 17, 14, 22, 15, 16, 17, 14, 12. 2. **Mean** is the average of the numbers. Formula: $$\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total count}}$$ 3. Calculate the sum: $$17 + 18 + 16 + 17 + 17 + 14 + 22 + 15 + 16 + 17 + 14 + 12 = 191$$ 4. Count the numbers: There are 12 numbers. 5. Calculate mean: $$\frac{191}{12} \approx 15.92$$ 6. **Median** is the middle value when numbers are arranged in order. 7. Arrange numbers in ascending order: $$12, 14, 14, 15, 16, 16, 17, 17, 17, 17, 18, 22$$ 8. Since there are 12 numbers (even), median is average of 6th and 7th numbers: $$\frac{16 + 17}{2} = 16.5$$ 9. **Mode** is the number that appears most frequently. 10. Count frequencies: 17 appears 4 times, which is the highest. 11. So, mode = 17. 12. **Problem 2: Speed to cover same distance in 1 2/3 hours if speed is 840 km/hr for 6 hours.** 13. Use formula: $$\text{Distance} = \text{Speed} \times \text{Time}$$ 14. Calculate distance: $$840 \times 6 = 5040 \text{ km}$$ 15. Convert mixed number to improper fraction: $$1 \frac{2}{3} = \frac{5}{3} \text{ hours}$$ 16. Find required speed: $$\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{5040}{\frac{5}{3}} = 5040 \times \frac{3}{5} = 3024 \text{ km/hr}$$ 17. **Problem 3: Sweets divided among 24 children, each gets 5 sweets. How many sweets each if children reduced by 4?** 18. Total sweets: $$24 \times 5 = 120$$ 19. New number of children: $$24 - 4 = 20$$ 20. Sweets per child now: $$\frac{120}{20} = 6$$ 21. **Problem 4: Harry and Joe mop warehouse together in 8 hours. Harry alone takes 12 hours. Find Joe's time alone.** 22. Work rates: Harry's rate $$= \frac{1}{12}$$ per hour, together rate $$= \frac{1}{8}$$ per hour. 23. Joe's rate: $$\frac{1}{8} - \frac{1}{12} = \frac{3}{24} - \frac{2}{24} = \frac{1}{24}$$ per hour. 24. Joe's time alone: $$\frac{1}{\frac{1}{24}} = 24 \text{ hours}$$ 25. AI tools like ChatGPT and WolframAlpha were used to verify calculations and understand formulas for mean, median, mode, speed-distance-time relations, and work-rate problems. They helped confirm intermediate steps and final answers, ensuring accuracy and clarity in explanations.