There is something wrong with this question. It should be 30 minutes after the two set off, the dog began to chase the first person and then ran back and forth, so it can be worked out. Otherwise, the dog will start shooting there, because the dog is much faster, and it will take some time to catch up.

Suppose after a while, the dog starts chasing the first person, then

Suppose time t 1, (6-2)t 1=2a, t 1=a/2.

Suppose we catch up with the second person t2,

(6-4)t2=4*(a+t 1), t2=3a, the distance from the first person at this time.

=2*(a+t 1+t2)，

The final distance in the future =2*(a+t 1+t2+t3+ ...)

Because the limit of a tends to 0, t 1+t2+t3+...= 1, then the final distance = 2 (0+ 1) = 2km.

So after 1 hour, the distance from the first person is 2 kilometers.