1. **State the problem:** We have a map scale of 1 : 120000, meaning 1 cm on the map represents 120000 cm in real life. **a)** Find the real-life distance from the waterfall to the beach. **b)** Find the map distance in cm between the waterfall and the mountains if the real-life distance is 6 km. 2. **Formula and rules:** - Real distance = Map distance $ \times $ Scale factor - Map distance = Real distance $ \div $ Scale factor - Convert units carefully: 100 cm = 1 m, 1000 m = 1 km 3. **Part a) Distance from waterfall to beach:** - Map distance = 8 cm - 1 cm = 7 cm - Real distance in cm = $7 \times 120000 = 840000$ cm - Convert to km: $840000 \text{ cm} = \frac{840000}{100} \text{ m} = 8400 \text{ m} = \frac{8400}{1000} = 8.4$ km 4. **Part b) Distance from waterfall to mountains on the map:** - Real distance = 6 km = $6 \times 1000 \times 100 = 600000$ cm - Map distance = $\frac{600000}{120000} = 5$ cm **Final answers:** - a) The real-life distance from the waterfall to the beach is **8.4 km**. - b) The distance on the map between the waterfall and the mountains is **5 cm**.