A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, his speed (in km/hr) must be

### Concept & Formula The core concept is calculating the required speed for the second leg of a journey given the total constraints and the first leg's performance. $$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $$ ### Step-by-Step Solution * **Given:** * Total distance = $6$ km * Total time = $45$ minutes * **Calculation for First Half:** * Distance covered = $\frac{1}{2} \times 6 = 3$ km * Time taken = $\frac{2}{3} \times 45 = 30$ minutes * **Calculation for Remaining Journey:** * Remaining distance = $6 - 3 = 3$ km * Remaining time = $45 - 30 = 15$ minutes * **Final Speed Calculation:** * Convert time to hours: $15$ minutes = $\frac{15}{60}$ hours = $\frac{1}{4}$ hour * Required Speed = $\frac{\text{Remaining Distance}}{\text{Remaining Time}} = \frac{3}{1/4} = 3 \times 4 = 12$ km/hr ### Exam Strategy & Shortcut Break the problem down into two distinct phases. Always convert minutes to hours before the final speed calculation if the options are in km/hr. ### Common Pitfall Forgetting to convert the remaining time from minutes to hours, which would lead to an incorrect speed of $3 / 15 = 0.2$ km/min, and possibly misinterpreting the options. ### Final Answer Therefore, the correct answer is **12**.