Question: 6
The scale of a street map is 1 : 5000. Find the actual distance, in metres, for the following distances on the map.
(a) 4 cm
(b) 7 cm
1. **Problem statement:**
Given a map scale of 1 : 5000, find the actual distances corresponding to map distances of 4 cm and 7 cm.
2. **Formula and explanation:**
The scale 1 : 5000 means that 1 cm on the map represents 5000 cm in reality.
To find the actual distance, use the formula:
$$\text{Actual distance} = \text{Map distance} \times \text{Scale factor}$$
3. **Convert scale factor to metres:**
Since 100 cm = 1 m, 5000 cm = \frac{5000}{100} = 50 \text{ metres}$$
4. **Calculate actual distances:**
(a) For 4 cm on the map:
$$\text{Actual distance} = 4 \times 50 = 200 \text{ metres}$$
(b) For 7 cm on the map:
$$\text{Actual distance} = 7 \times 50 = 350 \text{ metres}$$
5. **Final answers:**
(a) 200 metres
(b) 350 metres
This means that 4 cm on the map corresponds to 200 metres in reality, and 7 cm corresponds to 350 metres.