7.4. Masha and Misha set out to meet each other simultaneously, each from their own house, and met one kilometer from Masha's house. Another time, they again set out to meet each other simultaneously, each from their own house, but Masha walked twice as fast, and Misha walked twice as slow as the previous time. This time, they met one kilometer from Misha's house. What is the distance between Masha's and Misha's houses?
# Answer: 3 km.

Solution: We will prove that they spent the same amount of time on the first and second occasions. Suppose this is not the case, and they spent less time on the second occasion. Then, on the first occasion, Masha walked 1 km, and on the second occasion, less than 2 km (her speed was twice as high, but the time was less). Misha walked 1 km on the second occasion, so on the first occasion, he walked more than 2 km (for similar reasons). Therefore, the total distance is more than 3 km (1 km from Masha and more than 2 km from Misha on the first occasion), but at the same time, it is less than 3 km (1 km from Misha and less than 2 km from Masha on the second occasion). This is impossible. If they walked longer on the second occasion, similar reasoning will lead to a contradiction (due to the symmetry of the situations).

Thus, they moved for the same amount of time both times. Therefore, on the second occasion, Masha walked 2 km, and Misha walked 1 km. Consequently, their houses are 3 kilometers apart.

Criteria: answer, answer with verification - 0 points, not proven that the time was the same in the first and second cases, when using this - no more than 2 points.