1. Problem 12: A car travelling at 90 km/h is 500 m behind another car travelling at 70 km/h in the same direction. Find the time for the first car to catch the second. 2. Formula: Time = Distance / Relative Speed 3. Convert speeds from km/h to m/s: $$90 \text{ km/h} = \frac{90 \times 1000}{3600} = 25 \text{ m/s}$$ $$70 \text{ km/h} = \frac{70 \times 1000}{3600} = \frac{70000}{3600} = \frac{70000}{3600} \approx 19.44 \text{ m/s}$$ 4. Calculate relative speed: $$25 - 19.44 = 5.56 \text{ m/s}$$ 5. Calculate time to catch up: $$\text{Time} = \frac{500}{5.56} \approx 89.93 \text{ seconds}$$ --- 6. Problem 13: Find the length of a train passing a signal in 20 seconds at 108 km/h. 7. Formula: Length = Speed \times Time 8. Convert speed from km/h to m/s: $$108 \text{ km/h} = \frac{108 \times 1000}{3600} = 30 \text{ m/s}$$ 9. Calculate length: $$\text{Length} = 30 \times 20 = 600 \text{ meters}$$ Final answers: - Time for first car to catch second: approximately 90 seconds. - Length of the train: 600 meters.