13.304. Two meshing gears $A$ and $B$ are mounted tightly: the first on shaft $O_{1}$, and the second on shaft $O_{2}$. Gear $A$ has 10 more teeth than $B$. At a certain rotational speed of shaft $O_{1}$, shaft $O_{2}$ makes 63 revolutions per minute. If the gears are swapped, then at the same speed of shaft $O_{1}$, shaft $O_{2}$ makes 28 revolutions. Determine the number of teeth on each gear.
Solution.

Let gear $B$ have $x$ teeth, and $A-(x+10), V$ be the speed of shaft $O_{1}$. According to the condition, we have the system $\left\{\begin{array}{l}(x+10) V=63 x, \\ x V=28(x+10)\end{array}\right.$ from which $x=20$.

Answer: 20 and 30.