Problems on Trains – Find train length from two platform times: A train takes 24 s to cross a 480 m platform and 36 s to cross a 900 m platform. What is the length of the train?
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A360 m
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B400 m
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C390 m
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D430 m
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E320 m
Answer
Correct Answer: 360 m
Explanation
Introduction / Context:Two crossing scenarios with different platform lengths allow us to eliminate speed and solve for train length directly. Represent total distance as (L_train + L_platform) = v * t in each case and subtract the equations.
Given Data / Assumptions:
- (L + 480) = v * 24.
- (L + 900) = v * 36.
- Uniform speed v.
Concept / Approach:Subtracting the two equations removes L: (900 − 480) = v(36 − 24), yielding v. Substitute back to find L.
Step-by-Step Solution:420 = v * 12 ⇒ v = 35 m/s.From L + 480 = 35 * 24 = 840 ⇒ L = 360 m.
Verification / Alternative check:For the 900 m platform: L + 900 = 360 + 900 = 1260 m; time = 1260 / 35 = 36 s, valid.
Why Other Options Are Wrong:400, 390, 430, 320 m will not satisfy both time equations simultaneously with one constant speed.
Common Pitfalls:Adding times or lengths incorrectly; not recognizing that subtracting the equations isolates v immediately.
Final Answer:360 m