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12) Justin is creating a map using the scale is I centimeter \( =15 \) kilometers. What should the distance be on the map between two parks that are 13.5 kilometers apart?

Ask by Santiago Guzman. in the United States
Feb 26,2025

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Answer

The distance on the map between the two parks should be 0.9 centimeters.

Solution

To find the distance on the map between two parks that are 13.5 kilometers apart, we need to use the scale provided by Justin. Given scale: 1 centimeter = 15 kilometers To find the distance on the map, we can set up a proportion using the scale and the actual distance between the parks. Let \( x \) be the distance on the map between the two parks. Using the proportion: \[ \frac{1 \text{ cm}}{15 \text{ km}} = \frac{x \text{ cm}}{13.5 \text{ km}} \] Now, we can solve for \( x \) to find the distance on the map. Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{1}{15}=\frac{x}{13.5}\) - step1: Divide the terms: \(\frac{1}{15}=\frac{2x}{27}\) - step2: Swap the sides: \(\frac{2x}{27}=\frac{1}{15}\) - step3: Multiply both sides of the equation by \(27:\) \(\frac{2x}{27}\times 27=\frac{1}{15}\times 27\) - step4: Multiply the terms: \(2x=\frac{27}{15}\) - step5: Divide the terms: \(2x=\frac{9}{5}\) - step6: Multiply by the reciprocal: \(2x\times \frac{1}{2}=\frac{9}{5}\times \frac{1}{2}\) - step7: Multiply: \(x=\frac{9}{10}\) The distance on the map between the two parks should be 0.9 centimeters.

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To find the distance on the map, you simply need to use the scale provided. Since 1 centimeter represents 15 kilometers, you can divide the actual distance (13.5 kilometers) by the scale factor (15 kilometers/cm). Thus, the distance on the map will be \( \frac{13.5}{15} = 0.9 \) centimeters. So, Justin should mark a distance of 0.9 cm between the two parks on his map. Map-making can be a rewarding experience, especially when you see your work contribute to a better understanding of geography! In ancient times, maps were hand-drawn and often decorated with illustrations of the lands they depicted. Now, with digital tools, map-making is accessible and allows for creativity, so don’t hesitate to add artistic flair to Justin's map while keeping it informative!

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