2. The navigator in businessman Boris Mikhailovich's "Lexus" informs him how much longer it will take to reach the destination if he continues at the average speed from the start of the journey to the present moment. Boris Mikhailovich set off from home to the cottage. Halfway through the journey, the navigator reported that it would take 1 more hour to reach the destination. At this moment, tractor driver Vasya pulled out onto the road right in front of the "Lexus," and there was no way to overtake him. After Boris Mikhailovich had driven half of the remaining distance, the navigator reported that it would take 2 more hours to reach the destination. How many hours will it take for the businessman to arrive at the cottage after this, if he does not overtake the tractor driver? (The speed of the tractor is constant.)
Answer: In 5 hours. First solution. Let the distance from home to the cottage be 4 units of length. Then the average speed of the "Lexus" on the first half of the journey was 2 units/hour. Let $v$ units/hour be the speed of the tractor. Then the "Lexus" spent $1 / v$ hours on the third quarter of the journey, and its average speed for the first three quarters of the journey was 3/(1+1/v) units/hour. On the other hand, with this speed, the "Lexus" would travel the remaining quarter of the journey in 2 hours, from which $2(3 /(1+1 / v))=1$. Solving this equation, we find $v=1 / 5$, from which we get the answer. Second solution. When the navigator informed Boris Mikhailovich that he had 2 hours left to travel, he had a quarter of the journey left to travel. This means that the $3 / 4$ of the journey already traveled took him 6 hours. But Boris Mikhailovich traveled the first half of the journey in one hour, so he spent 5 hours following Vasya for the third quarter of the journey. The same amount of time will be spent on the remaining quarter.