Let x = the length (km) of the whole trail.
1st day:
(1/8)x = 0.125x traveled.
Remaining amount = (1 - 0.125)x = 0.875x
2nd day:
(4/7) of 0.875x = 0.5x traveled.
Remaining amount = (1 - 0.5)x = 0.5x
3rd day:
(1/3) of 0.5x = 0.1667x traveled + 8 km
The total fractional parts traveled is
0.125x + 0.5x + 0.1667x = 0.7917x
The remaining fractional shares is (1 - 0.7917)x = 0.2083x.
This is equal to the 8 km traveled, therefore
0.2083x = 8
x = 8/0.2083 = 38.406 km
Answer: 38.4 km (nearest tenth)
