Task 3 - 060813 A cycling race is held on a $1 \mathrm{~km}$ long circular track. At a certain time, cyclist $B$ has exactly $500 \mathrm{~m}$ lead over cyclist $A$. $A$ is traveling at a speed of $50 \mathrm{~km} / \mathrm{h}$, and $B$ at a speed of $45 \mathrm{~km} / \mathrm{h}$.

After how many minutes would $A$ catch up with cyclist $B$ for the first time, if both continue to ride at a constant speed?
$B$ initially has a lead of $500 \mathrm{~m}$. In the same time it takes $A$ to cover $500 \mathrm{~m}$, $B$ only covers $450 \mathrm{~m}$. A thus gains $50 \mathrm{~m}$. In total, he needs to make up $500 \mathrm{~m}$. Under the conditions of the problem, he achieves this in exactly 5 laps.

The total length of the distance covered in 5 laps is $5 \mathrm{~km}$. Therefore, $B$ is caught by $A$ in 6 minutes.