2. At the front of the cycling race column are cyclists Aco and Boro, riding side by side. They have so far outpaced the other cyclists that no one can catch them before the finish line. At $20 \mathrm{~km}$ before the finish, Aco's tire goes flat. Boro continues to the finish line at an average speed of $40 \mathrm{~km} / \mathrm{h}$. Aco lost 3 minutes fixing the tire, and then continued riding at an average speed of $45 \mathrm{~km} / \mathrm{h}$. Who won the race and by what distance?
Solution. Boro reached the goal in $\frac{20}{40}=0.5 h$, or $30 \mathrm{~min}$. Aco needed $\frac{20}{45} h+3 \min =\frac{89}{3} \min$. Since $\frac{89}{3}<30$, we conclude that the winner is Aco. Aco arrived before Boro by $30-\frac{89}{3}=\frac{1}{3} \mathrm{~min}=20 \mathrm{~s}$. In those 20 seconds, Boro had $\frac{20}{3600} \cdot 40=\frac{2}{9} \mathrm{~km}$ left to travel.