The scale of a map is 5m= 15 mi maps 8.2 actual____
8.2m/5m = x miles/15 miles
Solve for x.
To find the actual distance represented by a given distance on the map, you need to use the scale ratio. In this case, the scale ratio is 5m = 15mi.
To find the actual distance (let's call it AD) corresponding to the map distance (let's call it MD), you can use the following formula:
AD = (MD * Actual Scale) / Map Scale
In your case, the map distance is 8.2 units. The actual scale is the number of meters represented by each unit on the map, and the map scale is the number of miles represented by each unit on the map.
According to the given scale ratio, 5 meters on the map represents 15 miles in reality. So the actual scale is 5 meters per unit and the map scale is 15 miles per unit.
Plugging in the values into the formula:
AD = (8.2 * 5m) / 15 mi
Before we calculate the actual distance, we need to ensure that the units cancel out correctly. To do this, we can convert 15 miles to meters as follows:
1 mile = 1609.34 meters (approximately)
So, 15 miles = 15 * 1609.34 meters
Now, we can substitute the values and calculate the actual distance:
AD = (8.2 * 5m) / (15 mi * 1609.34 m/mi)
AD = (8.2 * 5m) / (24140.1 m)
AD = (41 m) / (24140.1 m)
Simplifying the expression:
AD ≈ 0.001699 meters or approximately 1.699 millimeters
Therefore, with the given map scale, 8.2 units on the map would represent an actual distance of around 1.699 millimeters.