4. Misha and Masha were traveling by train to Kirov. Misha was lying on the bunk, while Masha was looking out the window. "How far is it to Kirov?" Misha asked Masha at 12:00. "73 kilometers," Masha replied. To the same question asked at 12:15 and 12:45, Masha answered: "62 kilometers" and "37 kilometers." It is known that if the distance was not a whole number of kilometers, Masha rounded it to the nearest whole number each time (and if there were two such numbers, she rounded to either one at her discretion). Find the speed of the train, given that it was constant. List all possibilities and prove that there are no others.
Answer: 48 km/h. Solution: Since Masha rounded the distance to the nearest whole number each time, at 12:00 the distance to Kirov was no less than 72.5 and no more than 73.5 km, at 12:15 - no less than 61.5 and no more than 62.5 km, and at 12:45 - no less than 36.5 and no more than 37.5 km. Therefore, in 15 minutes from 12:00 to 12:15, the train traveled no less than 10 and no more than 12 km, and in 30 minutes from 12:15 to 12:45 - no less than 24 and no more than 26 km. Since 15 minutes is a quarter of an hour and 30 minutes is half an hour, the first indicates that the speed of the train is no less than \(10 \times 4 = 40\) km/h and no more than \(12 \times 4 = 48\) km/h, and the second - that it is no less than \(24 \times 2 = 48\) km/h and no more than \(26 \times 2 = 52\) km/h. The only speed that satisfies both conditions is 48 km/h.