We have been given that the scale of a map is 1 inch : 85 miles. On the map, a river is 14 inches long. We are asked to find the actual length of the river in miles.
We will use proportions to solve our given problem.
[tex]\frac{\text{Actual length}}{\text{Map length}}=\frac{85\text{ miles}}{\text{1 inch}}[/tex]
Upon substituting map length of river in above equation, we will get:
[tex]\frac{\text{Actual length}}{\text{14 inches}}=\frac{85\text{ miles}}{\text{1 inch}}[/tex]
[tex]\frac{\text{Actual length}}{\text{14 inches}}\times \text{14 inches}=\frac{85\text{ miles}}{\text{1 inch}}\times \text{14 inches}[/tex]
[tex]\text{Actual length}=85\text{ miles}\times 14[/tex]
[tex]\text{Actual length}=1190\text{ miles}[/tex]
Therefore, the actual length of river is 1190 miles.
