Question

a map shows the distance between toronto and montreal as 6 cm. the map has a verbal scale of 1 cm represents 50 km. calculate the real earth distance between toronto and montreal. problem 2 (ratio scale → earth distance) on a map, the distance between vancouver and calgary is 12 cm. the map uses a ratio scale of 1:1,000,000. calculate the actual earth distance between vancouver and calgary in kilometers.

Explanation:

Step1: Use scale - distance relationship for Toronto - Montreal

Given 1 cm on map represents 50 km in real life. Map distance is 6 cm. Multiply map distance by scale factor.
$6\times50 = 300$ (km)

Step2: Use ratio scale for Vancouver - Calgary

The ratio scale 1:1,000,000 means 1 cm on map represents 1,000,000 cm in real life. First convert real - life distance from cm to km.
1 km = 100,000 cm. Map distance is 12 cm. Real - life distance in cm is $12\times1000000=12000000$ cm.
Then convert to km: $\frac{12000000}{100000}=120$ km

Answer:

The real Earth distance between Toronto and Montreal is 300 km.
The actual Earth distance between Vancouver and Calgary is 120 km.