1. **State the problem:** A snail climbs a 30-foot wall. Each hour, it climbs 3 feet but slips down 2 feet. We need to find how long it takes to reach the top. 2. **Understand the movement:** Every hour, the snail effectively climbs $3 - 2 = 1$ foot, except for the last climb when it reaches or exceeds 30 feet and does not slip back. 3. **Calculate the effective progress:** The snail gains 1 foot per hour for all but the last climb. 4. **Calculate hours to reach just below the top:** The snail needs to reach 27 feet by the end of some hour because in the next hour it will climb 3 feet and reach or exceed 30 feet without slipping. 5. **Calculate hours to reach 27 feet:** Since the snail gains 1 foot per hour, it takes 27 hours to reach 27 feet. 6. **Add the last climb:** In the 28th hour, the snail climbs 3 feet from 27 to 30 feet and reaches the top. 7. **Final answer:** It takes the snail **28 hours** to reach the top of the wall.