Two trains 70 m and 80 m long run on parallel tracks in opposite directions at 68 km/h and 40 km/h, respectively. How many seconds will they take to completely pass each other?
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A5 seconds
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B10 seconds
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C12 seconds
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D6 seconds
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E8 seconds
Answer
Correct Answer: 5 seconds
Explanation
Introduction / Context:For two trains moving in opposite directions, relative speed is the sum of speeds. Distance to be covered to cross fully equals the sum of their lengths.
Given Data / Assumptions:
- L1 = 70 m; L2 = 80 m → total S = 150 m.
- v1 = 68 km/h; v2 = 40 km/h; opposite directions.
Concept / Approach:v_rel = (68 + 40) km/h = 108 km/h. Convert v_rel to m/s; t = S / v_rel_mps.
Step-by-Step Solution:
v_rel = 108 * 5/18 = 30 m/s.t = 150 / 30 = 5 s.Verification / Alternative check:Had they moved in the same direction, relative speed would be 28 km/h and the time would be much larger—this quick 5 s is consistent with opposing motion.
Why Other Options Are Wrong:6, 8, 10, 12 seconds arise from wrong relative speed or length sums.
Common Pitfalls:Forgetting to add lengths; using difference of speeds in opposite direction cases.
Final Answer:5 seconds