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 hiked 1/3 of the remaining trail and the last 8 km. How many km is the whole trail?
This problem was in my rsm hw??? and your answer was wrong btw........
WRONG WRONG
It WAS IN MY RSM YOU ARE WRONG FOOL
To find the length of the whole trail, we need to add up the distances hiked on each of the three days.
On the first day, they hiked 1/8 of the trail. Let's call the length of the whole trail T. So, on the first day, they hiked T/8 km.
On the second day, they hiked 4/7 of the remaining trail. The remaining trail after the first day would be (T - T/8) km. So, on the second day, they hiked (4/7) * (T - T/8) km.
On the third day, they hiked 1/3 of the remaining trail and an additional 8 km. The remaining trail after the second day would be (T - T/8) - (4/7) * (T - T/8) km. Simplifying this, we get (3/7) * (T - T/8). So, on the third day, they hiked (1/3) * (3/7) * (T - T/8) + 8 km.
Now, we can add up the distances hiked on each day to get the total length of the trail:
(T/8) + (4/7) * (T - T/8) + (1/3) * (3/7) * (T - T/8) + 8 = T
Simplifying this equation will give us the value of T, the length of the whole trail.
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
(3/7)(8) or 24/7 km
day 3
(1/3)(24/7) + 8
= 64/7
yeahhh!