1. Seeing a fox several meters away, the dog chased after it along a straight dirt road. The dog's jump is $23 \%$ longer than the fox's jump. There is a time interval during which both the fox and the dog make a whole number of jumps. Each time it turns out that the dog manages to make $t \%$ fewer jumps than the fox, where $\mathrm{t}$ is an integer. Assuming that all jumps, both of the dog and the fox, are the same, find the minimum value of $t$ for which the fox can escape from the dog.
Solution: Let $\mathrm{x}$ be the length of the fox's jump, and $y$ be the number of jumps it makes in some unit of time. Then $xy$ is the distance the fox covers in this time. The distance covered by the dog in the same time is $1.23 x\left(1-\frac{t}{100}\right) y$. The fox will escape from the dog if $1.23 x\left(1-\frac{t}{100}\right) y < xy$; simplifying, we get $1.23\left(1-\frac{t}{100}\right) < 1$; further simplifying, $\frac{23}{1.23} < \frac{t}{100}$; thus, $t > 18 \frac{86}{123}$, which means $t=19\%$.

Answer: 19.