The distance from A to B is 3^3/4 miles . The distance is divided into 5 equal tracks. Each track is divided into sections, each of which is 1/ 3 of a track. What is the length of each section?

1 answer

The distance from A to B is \( \frac{3^3}{4} \) miles. First, we calculate \( 3^3 \):

\[ 3^3 = 27 \]

Thus, the total distance is:

\[ \frac{27}{4} \text{ miles} \]

Next, this distance is divided into 5 equal tracks. To find the length of each track, we divide the total distance by 5:

\[ \text{Length of each track} = \frac{27/4}{5} = \frac{27}{4} \times \frac{1}{5} = \frac{27}{20} \text{ miles} \]

Each track is further divided into sections, each of which is \( \frac{1}{3} \) of a track. To find the length of each section, we divide the length of each track by 3:

\[ \text{Length of each section} = \frac{27/20}{3} = \frac{27}{20} \times \frac{1}{3} = \frac{27}{60} \]

Now, we simplify \( \frac{27}{60} \):

Both the numerator and denominator can be divided by 3:

\[ \frac{27 \div 3}{60 \div 3} = \frac{9}{20} \]

Thus, the length of each section is:

\[ \boxed{\frac{9}{20}} \text{ miles} \]