4. Vasya and his father are collecting mushrooms in the forest. Father told Vasya: “Go ahead along this straight path. I will quickly check the glade and catch up with you.” The father's step is $20 \%$ longer than Vasya's. They both walk at a constant speed and do not change the length of their steps. There is a period of time during which both the father and Vasya make a whole number of steps. Each time it turns out that the father has made $t \%$ fewer steps than Vasya. For what largest integer value of $\mathrm{t}$ will the father start to catch up with Vasya?
Solution. Let $\chi$ be the length of Vasya's step, $y$ be the number of steps he takes in the specified unit of time. Then $x y$ is the distance Vasya covers in this time, $1.2 x y\left(1-\frac{t}{100}\right)$ is the distance covered by his father. For Vasya and his father to start getting closer, the inequality $1.2 x y\left(1-\frac{t}{100}\right)>x y$ must hold. Simplifying, $\frac{6}{5}\left(1-\frac{t}{100}\right)>1 ; 1-\frac{t}{100}>\frac{5}{6} ; t<\frac{100}{6}$. The largest integer value satisfying the inequality is $\mathrm{t}=16 \%$.

Answer: 16.