2. Variant 1. At the intersection of perpendicular roads, a highway from Moscow to Kazan and a road from Vladimir to Ryazan intersect. Dima and Tolya set out with constant speeds from Moscow to Kazan and from Vladimir to Ryazan, respectively. When Dima passed the intersection, Tolya had 3500 meters left to reach it. When Tolya passed the intersection, Dima was 4200 meters away from it. How many meters will be between the boys when Dima has traveled 4200 meters from the moment Tolya crossed the intersection?
Answer: 9100.

Solution. When Tolya has traveled 3500 meters, Dima will have traveled 4200 meters, so at the moment when Dima is 8400 meters past the intersection, Tolya will be 3500 meters past the intersection. By the Pythagorean theorem, the distance between the boys is 9100 meters.