So, if you can't understand what author of the problem meant, you're not alone :o)

He meant the following: chukcha goes from A to B and he covers each K kilometers in H hours. But the speed whithin this interval is not constant: he can cover K minus eps kilometers within first second of H hours and remaining eps kilometers in the remaining time (and visa versa).

It leads to the problem itself: what speed distribution along the interval leads to the minimum time to reach destination and what distribution leads to maximum time.

Thank you for your explanation.
And it turns out that the deer can cover K kilometers in 0.0000000001 second. hehe.

Thanks

The problem is just from Russia. Pay attention, the Chukchi is running, not an Eskimo, not an Indian, but a Chukchi. And in Russia everything is relative. And the position of the Chukchi is relative. That is, the Chukchi is located somewhere in the Yamal-Nenets district. On the territory within a radius of 100 kilometers from the telephone tower. In 2 hours he will be in an area within a radius of 100 kilometers from another telephone tower. That is, he will reach Moscow in 4 hours, plus or minus 2 hours. Something like this. Translation problems.