Two friends run a 3-kilometer race along a circular course of length 300 meters. If their speeds are in the ratio 3:2, the number of times the winner passes the other is

The winner passes the other runner $3$ times. When the winner completes $10$ laps, the other runner has completed $\frac{20}{3}$ laps, so the winner has gained $\frac{10}{3}$ laps. Each complete lap gained corresponds to one pass. Counting the simultaneous start gives $4$.