A map is drawn using the scale 2 cm:100 mi. On the map, Town B is 3.5 centimeters from Town A, and Town C is 2 centimeters past Town B. How many miles apart are Town A and Town C? A.) 275 miles B.) 200 miles C.) 550 miles D.) 1,100 miles
The Correct Answer and Explanation is:
- The map scale is 2 cm : 100 miles.
- Town B is 3.5 cm from Town A.
- Town C is 2 cm past Town B.
This means the total distance from Town A to Town C is: 3.5 cm (A to B)+2 cm (B to C)=5.5 cm3.5 \text{ cm (A to B)} + 2 \text{ cm (B to C)} = 5.5 \text{ cm}3.5 cm (A to B)+2 cm (B to C)=5.5 cm
Now, apply the scale to convert this map distance to real-world miles: If 2 cm=100 miles, then 1 cm=1002=50 miles\text{If 2 cm} = 100 \text{ miles}, \text{ then } 1 \text{ cm} = \frac{100}{2} = 50 \text{ miles}If 2 cm=100 miles, then 1 cm=2100=50 miles
Now multiply: 5.5 cm×50 miles/cm=275 miles5.5 \text{ cm} \times 50 \text{ miles/cm} = 275 \text{ miles}5.5 cm×50 miles/cm=275 miles
✅ Correct Answer: A.) 275 miles
Explanation
This problem involves interpreting a map scale and applying it to measure the real-world distance between three towns. A map scale gives the ratio between distances on the map and the actual distances they represent on the ground. In this case, the scale is 2 cm : 100 miles, which tells us that every 2 centimeters on the map equals 100 real-world miles. To make calculations easier, we simplify this to 1 cm : 50 miles.
Town B is 3.5 cm away from Town A on the map. That means the distance between Town A and Town B in real life is: 3.5 cm×50 miles/cm=175 miles3.5 \, \text{cm} \times 50 \, \text{miles/cm} = 175 \, \text{miles}3.5cm×50miles/cm=175miles
Then, the problem states that Town C is 2 cm past Town B, which implies Town C is an additional 2 cm away in the same direction. So the total map distance from Town A to Town C is: 3.5 cm+2 cm=5.5 cm3.5 \, \text{cm} + 2 \, \text{cm} = 5.5 \, \text{cm}3.5cm+2cm=5.5cm
We convert this total map distance to miles: 5.5 cm×50 miles/cm=275 miles5.5 \, \text{cm} \times 50 \, \text{miles/cm} = 275 \, \text{miles}5.5cm×50miles/cm=275miles
Therefore, the real-world distance between Town A and Town C is 275 miles. This demonstrates the importance of understanding how to interpret and use map scales to calculate actual distances. It also shows that small differences on a map can represent large distances in reality, depending on the scale used.
