7. The dog is chasing a rabbit that is 90 of its own jumps ahead of it. While the rabbit jumps 6 times, (20) the dog jumps only 5 times, and two dog jumps are as long as three rabbit jumps. How many jumps will the rabbit make until the dog catches it?
Solution. The length of a dog's jump is equal to $\frac{3}{2}$ the length of a rabbit's jump, so 4 dog jumps are equal to the length of 6 rabbit jumps.

(5 points)

While the rabbit jumps 6 times, the dog jumps 5 times, so in that time the dog covers a distance of $\frac{5}{6} \cdot \frac{3}{2}=\frac{5}{4}$ rabbit jumps.

(5 points)

If $x$ is the number of rabbit jumps, from the equation $90+x=\frac{5}{4} x$ we get $x=360$. The dog will catch the rabbit after 360 rabbit (or 300 dog jumps).

(10 points)