QUESTION 2 2.1 Determine the LCM and HCF of the numbers 20 and 45 . 2.2 A motorist covers a distance of 360 Km in exactly 4 hours. 2.2. How far did the motorist drive in 1 hour? 2.2.2 How far will the motorist drive in 7 hours? 2.2.3 How long will the motorist need to travel 900 Km ?

To find the LCM (Least Common Multiple) and HCF (Highest Common Factor) of 20 and 45, let’s break it down! The prime factorization of 20 is 2² × 5, and for 45, it’s 3² × 5. The HCF is found by taking the lowest power of the common factors, which gives us 5. The LCM is calculated by taking the highest powers, resulting in 2² × 3² × 5 = 180. Now, onto the motorist's journey! If the motorist covers 360 Km in 4 hours, they're driving at a splendid speed of 90 Km/h. So, in just 1 hour, the motorist zips through 90 Km! For the 7-hour adventure, just multiply that speed by the time: 90 Km/h × 7 hours equals a whopping 630 Km. Lastly, if they want to reach 900 Km, you simply divide the distance by the speed: 900 Km ÷ 90 Km/h = 10 hours of cruising! Buckle up!