Question

The scale on a map is 5 centimeters = 75 kilometers. Two lakes on the map are located 8.1 cm apart. What is the actual distance between the two lakes?

Answer 1

If 5 centimeters on the map represent 75 kilometers in the real world, then we can use proportion to find the actual distance between the two lakes.

Let x be the actual distance between the two lakes in kilometers. Then we can set up the following proportion:

5 cm / 75 km = 8.1 cm / x km

To solve for x, we can cross-multiply:

5 cm * x km = 75 km * 8.1 cm

Simplifying:

5x = 607.5

x = 121.5 km

Therefore, the actual distance between the two lakes is 121.5 kilometers.

Answer 2

We know that 5 centimeters on the map corresponds to 75 kilometers in real life. Therefore, we can set up a proportion to find out how many kilometers 1 centimeter on the map corresponds to:

5 cm / 75 km = 1 cm / x km

Cross-multiplying, we get:

5x = 75

Dividing both sides by 5, we get:

x = 15

So, 1 centimeter on the map corresponds to 15 kilometers in real life.

Now, we can use this information to find the actual distance between the two lakes. We know that they are located 8.1 cm apart on the map, so:

8.1 cm * 15 km/cm = 121.5 km

Therefore, the actual distance between the two lakes is 121.5 kilometers.