A person wishes to reach his destination 90 km away in 3 hours but for the first half of the journey his speed was 20 km/hr. His average speed for the rest of the journey should be

### Concept & Formula This problem tests your ability to track time and distance accurately, and critically, checks your attention to units in the final options. $$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $$ ### Step-by-Step Solution * **Given:** * Total distance = $90$ km * Total time available = $3$ hours * **First Half of Journey:** * Distance = $\frac{90}{2} = 45$ km * Speed = $20$ km/hr * Time taken = $\frac{45}{20} = 2.25$ hours * **Remaining Journey:** * Remaining distance = $90 - 45 = 45$ km * Remaining time = $3 - 2.25 = 0.75$ hours * **Required Speed:** * Speed = $\frac{45}{0.75} = \frac{4500}{75} = 60$ km/hr * **Unit Conversion:** * Notice that $60$ km/hr is not in the options (A is 40). Look at options B and C which are in km/min. * Convert $60$ km/hr to km/min: $\frac{60\text{ km}}{60\text{ mins}} = 1$ km/min. ### Exam Strategy & Shortcut Once you get $60$ km/hr, quickly scan the options. A common trap is selecting "None of these" when a unit conversion of the correct answer is present. Always check units! ### Common Pitfall Calculating $60$ km/hr, not seeing it in options (a), and immediately choosing "None of these" without checking the alternative units in options (b) and (c). ### Final Answer Therefore, the correct answer is **1 km/min**.