1. **Problem statement:** A van travels from station A to B at 40 km/hr and returns from B to A at 120 km/hr. We need to calculate: (i) Average speed for the round trip. (ii) Average velocity for the round trip. 2. **Formulas and rules:** - Average speed is total distance divided by total time. - Average velocity is total displacement divided by total time. - Since the van returns to the starting point, total displacement is zero. 3. **Calculations:** Let the distance between A and B be $d$ km. - Time from A to B: $t_1 = \frac{d}{40}$ hours. - Time from B to A: $t_2 = \frac{d}{120}$ hours. - Total distance: $2d$ km. - Total time: $t_1 + t_2 = \frac{d}{40} + \frac{d}{120} = \frac{3d + d}{120} = \frac{4d}{120} = \frac{d}{30}$ hours. 4. **Average speed:** $$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{2d}{\frac{d}{30}} = 2d \times \frac{30}{d} = 60 \text{ km/hr}$$ 5. **Average velocity:** - Total displacement is zero because the van returns to the starting point. - Therefore, average velocity is: $$\text{Average velocity} = \frac{0}{\text{Total time}} = 0 \text{ km/hr}$$ **Final answers:** (i) Average speed = 60 km/hr (ii) Average velocity = 0 km/hr