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Find the time taken by two trains, one 180 m long and the other 270 m long, to cross each other, if they are running at speeds of 46 kmph and 54 kmph respectively. Consider both possible cases of motion.
- a)202.5, 16.2 sec
- b)160, 100 sec
- c)108.45, 15.6 sec
- d)204.5, 14.8 sec
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Find the time taken by two trains, one 180 m long and the other 270 m ...
Case I: Motion in same direction
=>Relative speed = 54 — 46 = 8 km/hr.
Distance to be covered = 180 + 270 = 450 m.
=>Time = 0.450/8 = 0.056 hrs = 202.5 sec.
Case II: Motion in opposite direction.
=> Relative Speed = 54 + 46=100 km/hr.
Distance to be covered = 180 + 270= 450 m.
=>Time = 0.450/100 = 0.00045 hrs = 16.2 sec.
Most Upvoted Answer
Find the time taken by two trains, one 180 m long and the other 270 m ...
Given data:
- Length of first train (L1) = 180 m
- Length of second train (L2) = 270 m
- Speed of first train (S1) = 46 kmph
- Speed of second train (S2) = 54 kmph
Approach:
- When the two trains are moving in the same direction, the relative speed is the difference between the speeds of the two trains.
- When the two trains are moving in opposite directions, the relative speed is the sum of the speeds of the two trains.
Case a: Trains moving in the same direction
- Relative speed = 54 kmph - 46 kmph = 8 kmph = 8 * 5/18 m/s = 20/9 m/s
- Total distance to be covered = 180 m + 270 m = 450 m
- Time taken = Total distance / Relative speed = 450 / (20/9) = 202.5 seconds
Case b: Trains moving in the opposite direction
- Relative speed = 54 kmph + 46 kmph = 100 kmph = 100 * 5/18 m/s = 250/9 m/s
- Total distance to be covered = 180 m + 270 m = 450 m
- Time taken = Total distance / Relative speed = 450 / (250/9) = 16.2 seconds
Conclusion:
- The time taken for the two trains to cross each other is 202.5 seconds when they are moving in the same direction and 16.2 seconds when they are moving in opposite directions.
- Length of first train (L1) = 180 m
- Length of second train (L2) = 270 m
- Speed of first train (S1) = 46 kmph
- Speed of second train (S2) = 54 kmph
Approach:
- When the two trains are moving in the same direction, the relative speed is the difference between the speeds of the two trains.
- When the two trains are moving in opposite directions, the relative speed is the sum of the speeds of the two trains.
Case a: Trains moving in the same direction
- Relative speed = 54 kmph - 46 kmph = 8 kmph = 8 * 5/18 m/s = 20/9 m/s
- Total distance to be covered = 180 m + 270 m = 450 m
- Time taken = Total distance / Relative speed = 450 / (20/9) = 202.5 seconds
Case b: Trains moving in the opposite direction
- Relative speed = 54 kmph + 46 kmph = 100 kmph = 100 * 5/18 m/s = 250/9 m/s
- Total distance to be covered = 180 m + 270 m = 450 m
- Time taken = Total distance / Relative speed = 450 / (250/9) = 16.2 seconds
Conclusion:
- The time taken for the two trains to cross each other is 202.5 seconds when they are moving in the same direction and 16.2 seconds when they are moving in opposite directions.
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Find the time taken by two trains, one 180 m long and the other 270 m long, to cross each other, if they are running at speeds of 46 kmph and 54 kmph respectively. Consider both possible cases of motion.a)202.5, 16.2 secb)160, 100 secc)108.45, 15.6 secd)204.5, 14.8 secCorrect answer is option 'A'. Can you explain this answer?
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Find the time taken by two trains, one 180 m long and the other 270 m long, to cross each other, if they are running at speeds of 46 kmph and 54 kmph respectively. Consider both possible cases of motion.a)202.5, 16.2 secb)160, 100 secc)108.45, 15.6 secd)204.5, 14.8 secCorrect answer is option 'A'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the time taken by two trains, one 180 m long and the other 270 m long, to cross each other, if they are running at speeds of 46 kmph and 54 kmph respectively. Consider both possible cases of motion.a)202.5, 16.2 secb)160, 100 secc)108.45, 15.6 secd)204.5, 14.8 secCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the time taken by two trains, one 180 m long and the other 270 m long, to cross each other, if they are running at speeds of 46 kmph and 54 kmph respectively. Consider both possible cases of motion.a)202.5, 16.2 secb)160, 100 secc)108.45, 15.6 secd)204.5, 14.8 secCorrect answer is option 'A'. Can you explain this answer?.
Find the time taken by two trains, one 180 m long and the other 270 m long, to cross each other, if they are running at speeds of 46 kmph and 54 kmph respectively. Consider both possible cases of motion.a)202.5, 16.2 secb)160, 100 secc)108.45, 15.6 secd)204.5, 14.8 secCorrect answer is option 'A'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the time taken by two trains, one 180 m long and the other 270 m long, to cross each other, if they are running at speeds of 46 kmph and 54 kmph respectively. Consider both possible cases of motion.a)202.5, 16.2 secb)160, 100 secc)108.45, 15.6 secd)204.5, 14.8 secCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the time taken by two trains, one 180 m long and the other 270 m long, to cross each other, if they are running at speeds of 46 kmph and 54 kmph respectively. Consider both possible cases of motion.a)202.5, 16.2 secb)160, 100 secc)108.45, 15.6 secd)204.5, 14.8 secCorrect answer is option 'A'. Can you explain this answer?.
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