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A train 525 meters long running at a speed of 103 kmph overtakes another train which is 425 meters long running at a speed of 73 kmph in the same direction. Find the time taken by the faster train to overtake the slower train. (In seconds)
  • a)
    118
  • b)
    116
  • c)
    120
  • d)
    114
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A train 525 meters long running at a speed of 103 kmph overtakes anoth...
Given:
Length of the faster train = 525 m
Length of the slower train = 425 m
Speed of the faster train = 103 kmph
Speed of the slower train = 73 kmph
Formula used:
Speed = Distance/time
Speed in m/s = speed in kmph
Calculation:
Total distance = 525 + 425 = 950 m
When trains running in the same direction, then their relative speed is the difference between their speeds
⇒ Net speed = 103 - 73 = 30 kmph
⇒ Speed in m/s = 30 = 25/3 m/s
Total time =
⇒ Time = 38 × 3 = 114
∴ The time taken by the faster train to overtake the slower train = 114 s
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Most Upvoted Answer
A train 525 meters long running at a speed of 103 kmph overtakes anoth...
Understanding the Problem
To determine the time taken by the faster train to overtake the slower train, we need to first establish the effective speed at which the faster train is gaining on the slower one.
Step 1: Convert Speeds from km/h to m/s
- Faster train speed: 103 km/h
- (103 * 5/18) = 28.61 m/s
- Slower train speed: 73 km/h
- (73 * 5/18) = 20.28 m/s
Step 2: Calculate Relative Speed
- Relative speed = Speed of faster train - Speed of slower train
- 28.61 m/s - 20.28 m/s = 8.33 m/s
Step 3: Calculate Total Distance to be Covered
- When one train overtakes another, it must cover its own length plus the length of the other train.
- Total distance = Length of faster train + Length of slower train
- 525 m + 425 m = 950 m
Step 4: Calculate Time Taken to Overtake
- Time = Distance / Speed
- Time = 950 m / 8.33 m/s ≈ 114 seconds
Final Result
The time taken by the faster train to overtake the slower train is approximately 114 seconds, which corresponds to option 'D'.
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A train 525 meters long running at a speed of 103 kmph overtakes another train which is 425 meters long running at a speed of 73 kmph in the same direction. Find the time taken by the faster train to overtake the slower train. (In seconds)a)118b)116c)120d)114Correct answer is option 'D'. Can you explain this answer?
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