a) on a map the scale used is 1: 10,000. if two towns are separated by a straight 2.5 km road, what will be the distance between them on the map?
b) on a map 2.5 km is represented as 0.5 cm. what scale is being used on the map?
thanks heaps!
(a) 2.5km/10^4 = 2.5*10^5cm/10^4 = 25 cm
.5cm:2.5km = .5:2.5*10^5 = 1:5*10^5 = 1:500,000
Just as a check, the 1:10,000 scale used 25cm, and .5cm is 1/50 of that, so the scale should be 1:500,000
a) To determine the distance between two towns on a map using a specific scale, you can use the concept of proportions.
In this case, the scale used on the map is 1:10,000, which means that one unit on the map represents 10,000 units in reality.
Given that the distance between the two towns in reality is 2.5 km, we can set up a proportion to find the corresponding distance on the map:
1 unit on the map / 10,000 units in reality = x units on the map / 2.5 km
To solve for x, we can cross-multiply and divide:
x = (1 unit on the map / 10,000 units in reality) * 2.5 km
x = 2.5 km / 10,000
x = 0.00025 km
Therefore, the distance between the two towns on the map would be 0.00025 km.
b) To determine the scale being used on a map based on a given distance representation, you can set up a proportion again.
In this case, the map represents 2.5 km as 0.5 cm.
Using the same concept of proportions as before, we set up the equation:
1 unit on the map / x units in reality = 0.5 cm / 2.5 km
To solve for x (the units in reality per unit on the map), we can cross-multiply and divide:
x = (1 unit on the map / 0.5 cm) * 2.5 km
x = 2.5 km / 0.5 cm
x = 5 km/cm
Therefore, the scale being used on the map is 1:5,000 on the ratio of 5 kilometers per centimeter.