Question

6 tyler has two different maps of ohio. on the first map, the scale is 1 cm to 10 km. the distance from cleveland to cincinnati is 40 cm. on the second map, the scale is 1 cm to 50 km. what is the distance from cleveland to cincinnati on the second map? explain your reasoning.

Explanation:

Step1: Calculate the actual distance

The scale of the first map is \(1\) cm to \(10\) km and the map - distance is \(40\) cm.
Using the formula \( \text{Actual distance}=\text{Map distance}\times\text{Scale factor}\), we have \( \text{Actual distance}=40\times10 = 400\) km.

Step2: Calculate the map - distance on the second map

The scale of the second map is \(1\) cm to \(50\) km. Let the map - distance on the second map be \(x\) cm.
Using the formula \(x=\frac{\text{Actual distance}}{\text{Scale factor}}\), we substitute the actual distance (\(400\) km) and the scale factor of the second map (\(50\) km/cm). So \(x=\frac{400}{50}=8\) cm.

Answer:

The distance from Cleveland to Cincinnati on the second map is \(8\) cm.