1. Two trains, each containing 15 identical cars, were moving towards each other at constant speeds. Exactly 28 seconds after the first cars of the trains met, passenger Sasha, sitting in the third car, passed passenger Valera from the oncoming train, and another 32 seconds later, the last cars of these trains had completely passed each other. In which car, by count, was Valera traveling?

Answer: 12.
Solution. Since 60 seconds have passed from the moment the "zero" cars parted ways (which is also the moment the first cars met) to the moment the 15th cars parted ways, the next cars parted ways every $60: 15=4$ seconds. Therefore, after 28 seconds, the 7th cars of the trains had just parted ways, meaning the 7th car of one train had just aligned with the 8th car of the other. At this moment, Sasha's 3rd car aligned with Valery's car, which has the number $8+(7-3)=12$.