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II. Abby studies a map of Italy that shows a scale of \( 0.5 \mathrm{~cm}=10 \mathrm{~km} \). The Pantheon and the Spanish Steps are 0.4 cm apart on the map. The Trevi Fountain is located exactly half way between the Pantheon and the Spanish Steps. What is the distance in kilometers fram the Trevi fountain to the Spanish Steps?

Ask by Bolton Lee. in the United States
Feb 27,2025

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Answer

The distance from the Trevi Fountain to the Spanish Steps is 4 kilometers.

Solution

We are given that 0.5 cm corresponds to 10 km on the map. First, determine the actual distance between the Pantheon and the Spanish Steps:   Distance = (0.4 cm) × (10 km / 0.5 cm) = 0.4/0.5 × 10 km = 0.8 × 10 km = 8 km. Since the Trevi Fountain is exactly halfway between them, the distance from the Trevi Fountain to the Spanish Steps is half of 8 km:   Half distance = 8 km ÷ 2 = 4 km. Thus, the distance from the Trevi Fountain to the Spanish Steps is 4 km.

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Bonus Knowledge

First, let’s get to the real distances using the map scale. If \(0.5 \, \text{cm}\) represents \(10 \, \text{km}\), then \(0.4 \, \text{cm}\) represents \( (0.4 \, \text{cm} \times 10 \, \text{km}) / 0.5 \, \text{cm} = 8 \, \text{km} \). Since the Trevi Fountain is halfway between the Pantheon and the Spanish Steps, it’s \(4 \, \text{km}\) from either location, including the Spanish Steps. So, the distance from the Trevi Fountain to the Spanish Steps is \(4 \, \text{km}\). To make it even more relatable, imagine strolling through the beautiful streets of Rome. As you enjoy gelato along the way, you’ll only need to walk about \(4 \, \text{km}\) to get from the Trevi Fountain to the charming Spanish Steps. A perfect excuse to soak in both the sights and tastes of this historic city!

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