1. Alice and the White Rabbit left the Rabbit's house together at noon and went to the Duchess's reception. Having walked halfway, the Rabbit remembered that he had forgotten his gloves and fan, and ran home for them at twice the speed he had walked with Alice. Grabbing the gloves and fan, he ran to the Duchess (at the same speed he ran home). As a result, Alice (who had been walking at a constant speed the whole time) arrived at the Duchess's on time, while the Rabbit was 10 minutes late. At what time was the reception at the Duchess's scheduled?
Answer: At 12:40. Solution: While running after his forgotten items, the Rabbit ran a distance equal to the path from his cottage to the reception area. Alice, walking at half the speed of the Rabbit, covered half of this distance in the same time. This means that when the Rabbit reached the halfway point, Alice had just arrived at the reception area. The 10 minutes by which the Rabbit was late were needed for him to cover the second half of the distance. Alice covered it at half the speed, i.e., in 20 minutes, and the entire distance in 40 minutes. This is how we arrive at the answer.