if a line 2.35 inches long on a map is equal to 1000m in the real world, what is distance in feet of a line 6.05 inches on the map?
The correct answer and explanation is:
Let’s solve this step-by-step:
Given:
- A line 2.35 inches on the map = 1000 meters in real life.
- Find the real-life distance in feet for a line 6.05 inches on the map.
Step 1: Find the scale factor (real distance per inch on the map)
Real distance per inch on map = 1000 meters2.35 inches=425.53 meters/inch\frac{1000 \text{ meters}}{2.35 \text{ inches}} = 425.53 \text{ meters/inch}
Step 2: Calculate the real-world distance corresponding to 6.05 inches on the map
6.05 inches×425.53 meters/inch=2573.11 meters6.05 \text{ inches} \times 425.53 \text{ meters/inch} = 2573.11 \text{ meters}
Step 3: Convert meters to feet
1 meter = 3.28084 feet, so 2573.11 meters×3.28084=8446.46 feet2573.11 \text{ meters} \times 3.28084 = 8446.46 \text{ feet}
Final Answer:
A line 6.05 inches on the map corresponds to approximately 8,446.46 feet in the real world.
Explanation (300 words):
When working with map scales and real-world distances, the key is to understand the ratio between the map measurement and the actual distance it represents. In this problem, 2.35 inches on the map represents 1000 meters in reality. This gives a scale factor indicating how many meters correspond to one inch on the map.
By dividing 1000 meters by 2.35 inches, we get the real-world meters per inch of the map line, which is approximately 425.53 meters per inch. This means that for every inch on the map, the real-world distance is about 425.53 meters.
Once the scale factor is known, we can easily find the real-world distance corresponding to any length on the map by multiplying the map measurement by the scale factor. In this case, multiplying 6.05 inches by 425.53 meters/inch gives about 2573.11 meters.
Since the problem asks for the distance in feet, a conversion from meters to feet is necessary. Knowing that 1 meter equals approximately 3.28084 feet allows for this conversion by multiplication. Multiplying the real-world distance in meters by 3.28084 converts the distance to feet.
This step-by-step process shows how to use proportional reasoning and unit conversion to interpret and calculate distances using map scales. This approach is useful in many real-world applications, such as geography, navigation, urban planning, and engineering, where accurate distance measurements based on maps are critical.
If you were to rely solely on the map measurement, the scale factor is your bridge to the actual distance in the real world, which then can be converted into any desired units, like feet in this case.