Question

1. the scale on a canadian road map is 1:700 000. a) what does this scale represent? b) determine the actual distance between two cities, in kilometres, if the distance on the map is 12 cm. c) determine the distance on the map, in centimetres, if the actual distance between two cities is 40 km.

Explanation:

Part (a)

A scale of \(1:700000\) means that \(1\) unit (e.g., \(1\) cm) on the map represents \(700000\) of the same units (e.g., \(700000\) cm) in real life.

Step 1: Recall the scale meaning

The scale \(1:700000\) means \(1\) cm on the map \( = 700000\) cm in actual distance.

Step 2: Calculate actual distance in cm

If the map distance is \(12\) cm, actual distance \(d = 12\times700000\) cm \( = 8400000\) cm.

Step 3: Convert cm to km

Since \(1\) km \( = 100000\) cm, divide by \(100000\): \(\frac{8400000}{100000}=84\) km.

Step 1: Convert actual distance to cm

Actual distance is \(40\) km. Since \(1\) km \( = 100000\) cm, \(40\) km \( = 40\times100000 = 4000000\) cm.

Step 2: Use the scale to find map distance

Let map distance be \(x\) cm. From scale \(1:700000\), \(\frac{1}{700000}=\frac{x}{4000000}\). Solve for \(x\): \(x=\frac{4000000}{700000}\approx5.71\) cm (or \(\frac{40}{7}\) cm).

Answer:

The scale \(1:700000\) means \(1\) unit on the map represents \(700000\) units in actual distance.

Part (b)