2. The cities $A$ and $B$ are $106 \mathrm{~km}$ apart. At noon, from city $A$, Antonio set off on a bicycle heading towards $B$ at a constant speed of $30 \mathrm{~km} / \mathrm{h}$. Half an hour later, from city $B$, Bojan set off on foot heading towards $A$ at a constant speed of $5 \mathrm{~km} / \mathrm{h}$. At the moment Antonio started heading towards $B$, a fly took off from his nose and flew towards $B$ at a constant speed of $50 \mathrm{~km} / \mathrm{h}$. When the fly met Bojan, it landed on his nose, and immediately flew back to Antonio at the same speed, landed on his nose, and immediately flew back to Bojan, and so on until Antonio and Bojan met. How many kilometers did the fly fly?
Solution. At 12:30, Antonio is at $106-15=91$ kilometers from $B$. At the same moment, Bojan starts from $B$. The time they need (measured from that moment) to meet is $\frac{91}{30+5}=\frac{91}{35}=\frac{13}{5}$ hours. Thus, the bird flies for half an hour (until 12:30) and another $\frac{13}{5}$ hours, at a speed of $50 \mathrm{~km} / \mathrm{h}$. During this time, it flies a total of $50 \cdot\left(\frac{1}{2}+\frac{13}{5}\right)=155$ kilometers.