That's just a really badly written question. Firstly, since it is a biathlon, you would assume that both legs of the race are equal length, and therefore solve these two simultaneous equations together:
4/5*x = 30
and (convert time from minutes to hours)
4/15(x+30) = 30
which gives 4/5*x = 4/15(x+30) , therefore x = 15 km/h.
However, if you just solve 4/5*x = 30 , you get x = 37.5 km/h. Therefore, you cannot travel an equal distance for both legs of the race and making that assumption would be wrong. (you can test that when x = 15 km/h, the distance is not 60 km)
Therefore, you have to solve for different lengths:
4/5*x + 4/15(x+30) = 60 , therefore x = 48.75 km/h
The correct answer to the question is that Kim runs at 48.75 km/h, but the question is super dodgy