Solution: In the time when the fox runs one step, the dog can run 3/5 steps (the fox runs 5 steps and the dog runs 3 steps).

A dog running one step is equivalent to a fox running 7/4 steps (the distance between a dog running 4 steps and a fox running 7 steps).

In this way, the fox runs one step and the dog runs (3/5)*(7*4)=2 1/20 steps.

In other words, the speed of the dog is 2 1/20 of that of the fox.

Suppose the dog catches up with the fox and the fox runs x meters, then the dog runs (2 1/20)*x distance.

We can establish the equation:

(2 1/20)x-x=30

The solution is x=600.

That is to say, when the dog catches up with the fox, the fox runs 600 meters, while the dog runs 600+30=630 meters (or 600*(2 1/20)=630).