2. Mikhail and Martin live at the same distance from the school and started for the school at the same time. Mikhail's step is $10 \%$ shorter than Martin's, but Mikhail took $10 \%$ more steps than Martin in the same time. Who arrived at the school first?
Solution. Let the length of Martin's step be $x$. Since $10\%$ of $x$ is $0.1 x$, we get that the length of Mikhail's step is $0.9 x$. Furthermore, if Martin has taken $y$ steps, since $10\%$ of $y$ is $0.1 y$, Mikhail has taken $1.1y$ steps. According to this, when Mikhail travels a distance of $x y$, then Martin travels a distance of $0.9 x \cdot 1.1 y = 0.99 x y < x y$, which means that Martin arrives at school first.