A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance (in km) is

### Concept & Equation Set up a total time equation based on equal distance segments. Always ensure units of time match before solving. $$ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $$ ### Step-by-Step Solution * **Given:** * Let each equal distance segment be $x$ km. * Total distance = $3x$ km. * Speeds are $3$, $4$, and $5$ km/hr. * Total time = $47$ minutes = $\frac{47}{60}$ hours. * **Equation Setup:** * $\frac{x}{3} + \frac{x}{4} + \frac{x}{5} = \frac{47}{60}$ * **Solve for $x$:** * LCM of $3, 4, 5$ is $60$. * $\frac{20x + 15x + 12x}{60} = \frac{47}{60}$ * $\frac{47x}{60} = \frac{47}{60}$ * $x = 1$ km * **Calculate Total Distance:** * Total distance = $3x = 3 \times 1 = 3$ km. ### Exam Strategy & Shortcut Assume the equal distance is the LCM of the speeds ($60$ km). The times would be $20$, $15$, and $12$ hours, totaling $47$ hours. Since the actual time is $47$ minutes ($\frac{47}{60}$ hours), the actual distance must be $\frac{1}{60}$ of our assumed distance. Distance per segment = $60 \times \frac{1}{60} = 1$ km. Total = $3 \times 1 = 3$ km. ### Common Pitfall Finding $x = 1$ and forgetting that the total distance is $3x$. Luckily, $1$ is not an option here, but this is a frequent trap. Also, forgetting to convert $47$ minutes to hours. ### Final Answer Therefore, the correct answer is **3**.