Question

Frankie visited a park that has a rectangular trail around its outer edge. The dimensions of the trail are shown below.

The left and right sides of a rectangle are labeled one-third mile, and the top and bottom sides of the rectangle are labeled two-fifths mile.

Frankie walked around the trail one time. How many miles did she walk? Type your response as a fraction or mixed number in the box below.

Answer 1

To find the total distance Frankie walked around the rectangular trail, we need to calculate the perimeter of the rectangle.

The formula for the perimeter \( P \) of a rectangle is given by:

\[
P = 2 \times (\text{length} + \text{width})
\]

From the information provided, we can identify the length and width:
- Width of the rectangle (left/right side) = one-third mile = \( \frac{1}{3} \) miles
- Length of the rectangle (top/bottom side) = two-fifths mile = \( \frac{2}{5} \) miles

Now, substituting these values into the perimeter formula:

\[
P = 2 \times \left(\frac{2}{5} + \frac{1}{3}\right)
\]

To add the fractions \( \frac{2}{5} \) and \( \frac{1}{3} \), we need a common denominator. The least common multiple of 5 and 3 is 15.

Now convert each fraction:
- For \( \frac{2}{5} \):
\[
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\]
- For \( \frac{1}{3} \):
\[
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
\]

Now we can add the two fractions:
\[
\frac{6}{15} + \frac{5}{15} = \frac{11}{15}
\]

Now we substitute this sum back into the perimeter formula:

\[
P = 2 \times \frac{11}{15} = \frac{22}{15}
\]

Thus, the total distance Frankie walked around the trail is:

\[
\frac{22}{15} \text{ miles}
\]

This can also be expressed as a mixed number:

\[
\frac{22}{15} = 1 \frac{7}{15}
\]

However, as the problem requests the answer in fraction form, we can conclude that:

**Frankie walked \( \frac{22}{15} \) miles.**