, 22.06.2019 21:00 george27212

# Tourists were on a hiking trip for three days. on the first day, they hiked 1/8 of the trail. on the second day they hiked 4/7 of the remaining trail. on the third day they hiked1/3 of the remaining trail and the last 8 km. how many km is the whole trail?

32 km is the answer! Hopes this helps

64/7 i think

Step-by-step explanation:

whole trip x km

day1 , hiked 1/8 of train, leaving (7/8)x

day 2 , hiked 4/7 of (7/8)x leaving

(3/7)(7/8)x or (3/8)x to be hiked

day3 :

(1/3)(3/8)x + 8 = x

x/8 + 8 = x

times 8

x + 64 = 8x

7x = 64

the trail is 64/7 km

check:

day 1 they hiked (1/8)(64/7)

leaving (7/8)(64/7) = 8 km

day2, hiked 4/7 of remaining, leaving

day 3

= 64/7

yeahhh!

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

38.4 km (nearest tenth)
Whole trip is 64/7 km I think.

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