We have been given that the scale on a trail map is 0.5 cm : 1 km. The straight distance between 2 huts on the trail is 16.9 cm. We are asked to find the actual distance between 2 huts.
We will use proportions to solve our given problem.
[tex]\frac{\text{Actual length}}{\text{Scale length}}=\frac{\text{1 km}}{\text{0.5 cm}}[/tex]
[tex]\frac{\text{Actual length}}{\text{16.9 cm}}=\frac{\text{1 km}}{\text{0.5 cm}}[/tex]
[tex]\frac{\text{Actual length}}{\text{16.9 cm}}\times \text{16.9 cm}=\frac{\text{1 km}}{\text{0.5 cm}}\times \text{16.9 cm}[/tex]
[tex]\text{Actual length}=\frac{\text{1 km}}{\text{0.5}}\times \text{16.9}[/tex]
[tex]\text{Actual length}=33.8\text{ km}[/tex]
Therefore, the actual distance between both huts is 33.8 km.
