I have a map with a scale of 2cm to 5 km. On the map, two towns are eight cm apart. What is the actual distance between the two towns?
well, if
2 cm ---> 5 km
1 cm ---> 2.5 km
then 8 cm ----> .......
To find the actual distance between the two towns, we need to convert the measurements on the map to real-world measurements. Let's start by calculating the scale ratio.
The scale ratio is determined by the relationship between the measurements on the map and the corresponding measurements in the real world. In this case, the scale is 2cm to 5 km.
To calculate the scale ratio, divide the real-world distance by the map distance. In this case, we have:
Scale ratio = 5 km / 2 cm
To convert the distance between the two towns on the map to the actual distance, we can set up a proportion using the scale ratio:
(map distance) / (actual distance) = (scale on the map) / (scale in the real world)
Let's plug in the known values:
8 cm / (actual distance) = 2 cm / 5 km
To find the actual distance, we can cross-multiply and then solve for (actual distance):
(8 cm) * (5 km) = (2 cm) * (actual distance)
40 cm * km = 2 cm * (actual distance)
Dividing both sides of the equation by 2 cm gives us:
(actual distance) = (40 cm * km) / 2 cm
Now, we need to convert the units to ensure consistency:
(actual distance) = (40 cm * km) / (2 cm) * (100,000 cm/km) [since there are 100,000 cm in 1 km]
Simplifying the equation:
(actual distance) = (40 * 100,000 cm) / 2 cm
(actual distance) = 2,000,000 cm / 2 cm
(actual distance) = 1,000,000 cm
Therefore, the actual distance between the two towns is 1,000,000 centimeters or 10 kilometers.