Answer :
To determine which track is longer, we compare the lengths of the opening track and the closing track. Here's the step-by-step analysis:
1. Convert the fractions to a common denominator for easy comparison:
- The opening track length is [tex]\(\frac{2}{5}\)[/tex] of an hour.
- The closing track length is [tex]\(\frac{1}{3}\)[/tex] of an hour.
- To compare these fractions, find a common denominator. The least common multiple of 5 and 3 is 15.
2. Convert each fraction to have a denominator of 15:
- For the opening track:
[tex]\[ \frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15} \][/tex]
- For the closing track:
[tex]\[ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \][/tex]
3. Compare the fractions:
- Now that both fractions have the same denominator, we can easily see which is larger by comparing their numerators:
[tex]\[ \frac{6}{15} \quad \text{(opening track)} \quad vs \quad \frac{5}{15} \quad \text{(closing track)} \][/tex]
- Since [tex]\(6 > 5\)[/tex], [tex]\(\frac{6}{15}\)[/tex] (the opening track) is longer than [tex]\(\frac{5}{15}\)[/tex] (the closing track).
4. Conclusion:
- The opening track, which is [tex]\(\frac{2}{5}\)[/tex] of an hour, is longer than the closing track, which is [tex]\(\frac{1}{3}\)[/tex] of an hour.
Therefore, the correct answer is:
Opening track
1. Convert the fractions to a common denominator for easy comparison:
- The opening track length is [tex]\(\frac{2}{5}\)[/tex] of an hour.
- The closing track length is [tex]\(\frac{1}{3}\)[/tex] of an hour.
- To compare these fractions, find a common denominator. The least common multiple of 5 and 3 is 15.
2. Convert each fraction to have a denominator of 15:
- For the opening track:
[tex]\[ \frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15} \][/tex]
- For the closing track:
[tex]\[ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \][/tex]
3. Compare the fractions:
- Now that both fractions have the same denominator, we can easily see which is larger by comparing their numerators:
[tex]\[ \frac{6}{15} \quad \text{(opening track)} \quad vs \quad \frac{5}{15} \quad \text{(closing track)} \][/tex]
- Since [tex]\(6 > 5\)[/tex], [tex]\(\frac{6}{15}\)[/tex] (the opening track) is longer than [tex]\(\frac{5}{15}\)[/tex] (the closing track).
4. Conclusion:
- The opening track, which is [tex]\(\frac{2}{5}\)[/tex] of an hour, is longer than the closing track, which is [tex]\(\frac{1}{3}\)[/tex] of an hour.
Therefore, the correct answer is:
Opening track
