4. A snowmobile and an ATV are competing on a winter circular track, a quarter of which is covered with loose snow, and the rest with packed snow. The snowmobile travels at 32 km/h over loose snow and 36 km/h over packed snow. The ATV travels at 16 km/h over loose snow and 48 km/h over packed snow. The snowmobile and the ATV start moving simultaneously at the beginning of the part of the track covered with loose snow and first travel along this part. Which of the vehicles will overtake the other first, and on which lap will this happen?
Answer: The snowmobile on its $11^{\text{th}}$ lap will overtake the quad on its $10^{\text{th}}$ lap.
Lomonosov Moscow State University

Lomonosov Olympiad in Mathematics for School Students

Final Stage 2019/2020 academic year for 11th grade

## Problem 7