Question

Tourists were on the hiking trip for three days. In the first day they walked 1/8 of the trail. On the second day they walked 4/7 of the remaining path. On the third day they walked 1/3 of the remaining trail and the last 8 km. How many km is the whole trail?

Answer 1

32 km.

Explanation:

Let us assume that the whole trail is x km.

So, on the first day the tourists walked
`(x)/(8)` km.

Then the remaining distance after first day is
`(x - (x)/(8)) = (7x)/(8)` km.

Now, on the second day the tourists walked
`(4)/(7)` of the remaining path i.e.
`(4)/(7) * (7x)/(8) = (x)/(2)` km.

So, the remaining path to travel after 2nd day is
`((7x)/(8) - (x)/(2)) = (3x)/(8)` km.

On the third day they walked
`(1)/(3)` of the remaining trail and last 8 km.

So,
`((3x)/(8) - (3x)/(8) * (1)/(3)) = 8`

⇒
`(x)/(4) = 8`

⇒ x = 32 km. (Answer)