Answer:
Length of the longest trail
![= 9 (1)/(3)](https://img.qammunity.org/2021/formulas/mathematics/high-school/duhm7u0azwcztmrdd2hpf1nsfzw9qp0zd3.png)
Explanation:
The length of the longest trail will be equal to product of the two trails.
Given -
Length of one trail
![= 5(1)/(3)](https://img.qammunity.org/2021/formulas/mathematics/high-school/xbd2icxmt1zz68z8ycvqs8k1bjqztd1e0u.png)
Length of the second trail
![= 1(3)/(4)](https://img.qammunity.org/2021/formulas/mathematics/high-school/rjzhhagrcpwiztg2h4czfy7492cf4765sl.png)
Re writing the fractions, we get -
Length of one trail
![= (16)/(3)](https://img.qammunity.org/2021/formulas/mathematics/high-school/36icjkf6mjlb4efcg3y3todxwuqgh3vy6f.png)
Length of second trail
![= (7)/(4)](https://img.qammunity.org/2021/formulas/mathematics/high-school/5o343uljxo7ni0dd1nloygzm178k7qp6wg.png)
The length of the longest trail
![(16)/(3) * (7)/(4)\\(16*7)/(3*4) \\(4*7)/(3) \\(28)/(3)\\9(1)/(3)](https://img.qammunity.org/2021/formulas/mathematics/high-school/r7rd4ictd8ej17mr0klybiogvnrud7jyhv.png)
Length of the longest trail
![= 9 (1)/(3)](https://img.qammunity.org/2021/formulas/mathematics/high-school/duhm7u0azwcztmrdd2hpf1nsfzw9qp0zd3.png)