A cellular service provider is expanding the number of cell towers it has in Sullivan County. On a map of the towers, there are two that are 42 centimeters apart. What is the actual distance between the two cell towers if the scale of the map is 14 centimeters = 1 kilometer?

Question

kilometers

Answer 1

To find the actual distance between the two cell towers, we need to use the scale of the map given as \(14\) centimeters = \(1\) kilometer.

First, we need to determine how many kilometers correspond to \(42\) centimeters on the map.

1. Set up a proportion using the scale: \[ \text{Scale: } 14 \text{ cm} \rightarrow 1 \text{ km} \]

2. Calculate the actual distance: \[ \text{Let } x \text{ be the actual distance in kilometers corresponding to } 42 \text{ cm.} \] We can set up the equation from the scale: \[ \frac{42 \text{ cm}}{14 \text{ cm}} = \frac{x \text{ km}}{1 \text{ km}} \]

   Simplifying the left side: \[ \frac{42}{14} = 3 \]

   This means: \[ x = 3 \text{ km} \]

So, the actual distance between the two cell towers is \( \boxed{3} \) kilometers.