time actually moving = 5h 10m - 30m = 4h 40m =14/3 h
let distance be x km
then x/3 + x/4 = 14/3
clearing fractions, 4x + 3x = 56
7x = 56
x = 8 km
ans: length of trail = 8 km
p.s.
i guess the sex change operation took place
in the half hour at the top !