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3.) A map is made of a park. The scale from the park to the map is 6 mi. To 1 cm. The length of Great Oaks Trail is 4.5 cm on this map. The scale from the same park to a different map is 8 mi. To 1 cm. The length of Salamander Trail is 3.5 cm on that map. Which is the longer trail, the Great Oaks Trail or the Salamander Trail?

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Answer:

Salamander Trail is longer than The Great Oaks Trail.

Step-by-step explanation:

Scale factor = [tex]\frac{\text{Dimensions of the park on map}}{\text{Actual dimensions of the park}}=\frac{1}{6}[/tex]

For the actual length of Great Oaks Trail,

[tex]\frac{4.5}{\text{Actual length of the Great Oaks Trail}}=\frac{1}{6}[/tex]

Actual length of Great Oaks Trail = 27 mi

Scale for the same park to the different map = [tex]\frac{1}{8}[/tex]

[tex]\frac{\text{Length of Salamander Trail on map}}{\text{Actual length of Salamander Trail}}=\frac{1}{8}[/tex]

[tex]\frac{3.5}{\text{Actual length of Salamander Trail}}=\frac{1}{8}[/tex]

Actual length of Salamander Trail = 8 × 3.5 = 28 mi.

Therefore, Salamander Trail is longer than The Great Oaks Trail.

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