A boy goes from his village to school at 3 km/h and returns at 2 km/h. If the total time for the round trip is 5 hours, what is the one-way distance between the village and the school?
Aptitude
Time and Distance
Difficulty: Easy
Choose an option
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A6 km
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B7 km
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C8 km
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D9 km
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E5 km
Answer
Correct Answer: 6 km
Explanation
Introduction / Context:For out-and-back journeys with different speeds over the same distance, total time is the sum of the two leg times using the same one-way distance.
Given Data / Assumptions:
- Forward speed = 3 km/h; return speed = 2 km/h.
- Total time (to and fro) = 5 h.
- Let one-way distance be D km.
Concept / Approach:Total time = D/3 + D/2. Solve for D.
Step-by-Step Solution:
D/3 + D/2 = 5D*(1/3 + 1/2) = 5 → D*(5/6) = 5D = 5 * (6/5) = 6 kmVerification / Alternative check:Times: 6/3 = 2 h out; 6/2 = 3 h back; total = 5 h as given.
Why Other Options Are Wrong:They do not satisfy the exact time equation with the stated speeds.
Common Pitfalls:Using average speed naively (e.g., arithmetic mean) instead of computing time per leg and summing.
Final Answer:6 km