To solve this problem, we need to understand the scale of the map, which is 6 cm : 20 km. This means that every 6 cm on the map corresponds to 20 km in reality.
First, let's calculate the actual distance represented by 1 cm on the map:
\[ \text{If } 6 \text{ cm represents } 20 \text{ km, then } 1 \text{ cm represents } \frac{20 \text{ km}}{6} = \frac{10}{3} \text{ km} \approx 3.33 \text{ km.} \]
Now we can apply this to each statement:
-
Two cities that are 15 cm apart on the map are actually 50 km apart.
- Actual distance = 15 cm * (20 km / 6 cm) = 15 * (20/6) km = 50 km.
- This statement is TRUE.
-
Two cities that are 50 cm apart on the map are actually 15 km apart.
- Actual distance = 50 cm * (20 km / 6 cm) = 50 * (20/6) km = 166.67 km.
- This statement is FALSE.
-
Two cities that are 10 cm apart on the map are actually 24 km apart.
- Actual distance = 10 cm * (20 km / 6 cm) = 10 * (20/6) km = 33.33 km.
- This statement is FALSE.
-
Two cities that are 240 cm apart on the map are actually 24 km apart.
- Actual distance = 240 cm * (20 km / 6 cm) = 240 * (20/6) km = 800 km.
- This statement is FALSE.
Based on the calculations, the only true statement is:
"Two cities that are 15 cm apart on the map are actually 50 km apart."