3. A dog2 was located at point A when it started to chase a fox at a distance of $30 \mathrm{~m}$ from $A$. The dog's jump is $2 \mathrm{~m}$, and the fox's jump is $1 \mathrm{~m}$. At the same time, while the dog makes two jumps, the fox makes three jumps. At what distance from $A$ will the dog catch the fox?
Solution. First method. Let $x$ be the distance from $A$ when the dog will catch the fox; then from the condition of the problem we will have:

$$
\frac{x}{4}=\frac{x-30}{3}
$$

from which we get $x=120$.

Thus, the dog will catch the fox at a distance of $120 \mathrm{~m}$ from $A$.

Second method. With two jumps, the dog approaches the fox by $2 \cdot 2-3 \cdot 1=1 \mathrm{~m}$. At the beginning, the fox is $30 \mathrm{~m}$ away, so for the dog to catch the fox, it needs to make $30 \cdot 2=60$ jumps, which means that from $A$ the dog will catch the fox at $60 \cdot 2=120 \mathrm{~m}$.