The average speed of a bus is one-third of the speed of a train. The train covers 1125 km in 15 hours. How much distance will the bus cover in 36 minutes?

### Concept & Unit Conversion in Distance When speeds and times are given in mixed units (hours vs minutes), they must be converted to a uniform metric before calculating final distances. $$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $$ $$ \text{Minutes to Hours} = \frac{\text{Minutes}}{60} $$ ### Step-by-Step Solution * **Find the speed of the train:** * $\text{Train Speed} = \frac{1125 \text{ km}}{15 \text{ hours}} = 75 \text{ km/hr}$. * **Find the speed of the bus:** The bus is one-third as fast as the train. * $\text{Bus Speed} = \frac{75}{3} = 25 \text{ km/hr}$. * **Convert the bus's travel time to hours:** * $36 \text{ minutes} = \frac{36}{60} \text{ hours} = \frac{3}{5} \text{ hours}$. * **Calculate the distance covered by the bus:** * $\text{Distance} = \text{Speed} \times \text{Time}$ * $\text{Distance} = 25 \times \frac{3}{5} = 5 \times 3 = 15 \text{ km}$. * Since 15 km is not present among options (a), (b), (c), or (d), the correct choice is "None of these". ### Exam Strategy & Shortcut To quickly divide 1125 by 15, break it down: $15 \times 100 = 1500$. $1125$ is $375$ less than $1500$. Since $15 \times 25 = 375$, the multiplier is $100 - 25 = 75$. Mental math techniques like this save time compared to scratchpad long division. ### Common Pitfall A major pitfall is failing to convert 36 minutes into hours. A student might mistakenly calculate Distance = $25 \times 36 = 900$ km, completely ignoring unit standardizations. ### Final Answer Therefore, the correct answer is **None of these**.