Question

Three members of a teen hiking group hiked 3
5
of the entire Appalachian trail. The hikers took turns carrying a backpack of supplies. If each teen carried the backpack the same distance, what part of the total distance did each hiker carry the backpack?

In this problem, the numerator is the same number as the
denominator
.
So the answer will be a
equivalent fraction
.
Each hiker carried the backpack for
1/3
of the total trail distance.

Answer 1

To determine what part of the total distance each hiker carried the backpack, we start with the total distance hiked by the three members of the hiking group, which is \( \frac{3}{5} \) of the entire Appalachian Trail.

Since there are three hikers and they each carried the backpack for an equal distance, we find the distance each hiker carried the backpack by dividing the total distance by the number of hikers:

\[
\text{Distance each hiker carried} = \frac{\frac{3}{5}}{3} = \frac{3}{5} \div 3 = \frac{3}{5} \times \frac{1}{3} = \frac{3 \times 1}{5 \times 3} = \frac{3}{15}
\]

Now we can simplify \( \frac{3}{15} \):

\[
\frac{3}{15} = \frac{1}{5}
\]

Thus, each hiker carried the backpack for \( \frac{1}{5} \) of the total distance of \( \frac{3}{5} \) of the entire Appalachian Trail.

In summary, each hiker carried the backpack for \( \frac{1}{5} \) of the total distance.