Two trains, same direction crossing time: Two trains of lengths 50 m and 65 m move in the same direction at 18 m/s and 17 m/s. Find the time taken by the faster train to completely cross the slower train.
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A100 s
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B114 s
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C95 s
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D115 s
Answer
Correct Answer: 115 s
Explanation
Introduction / Context:When two trains move in the same direction, the effective relative speed equals the difference of their speeds. To fully cross, the faster must cover the sum of lengths at this relative speed.
Given Data / Assumptions:
- Lengths: 50 m and 65 m
- Speeds: 18 m/s (faster) and 17 m/s (slower)
- Same-direction motion
Concept / Approach:Time = (total length to be cleared) / (relative speed). For same direction, relative speed = 18 − 17 = 1 m/s.
Step-by-Step Solution:
Total length = 50 + 65 = 115 mRelative speed = 18 − 17 = 1 m/sTime = 115 / 1 = 115 sVerification / Alternative check:Units consistent: metres / (metres per second) gives seconds. No conversion needed as speeds are already in m/s.
Why Other Options Are Wrong:100, 114, 95 are not equal to 115 computed from the standard crossing formula.
Common Pitfalls:Using sum of speeds (which applies to opposite directions) instead of difference for same-direction motion.
Final Answer:115 s