Two trains of 200 m and 100 m long are running parallel at the rate of 20 m/sec. and 22 m/sec. respectively. How much time will they take to cross each other, if the trains are running along the same direction?

Question

Two trains of 200 m and 100 m long are running parallel at the rate of 20 m/sec. and 22 m/sec. respectively. How much time will they take to cross each other, if the trains are running along the same direction? 

    (A) 212 sec. 

    (B) 135 sec. 

    (C) 150 sec. 

    (D) 120 sec.



Solution:

To find the time taken for two trains running in the same direction to cross each other, follow these steps:

  1. Determine the relative speed of the trains.

Since the trains are running in the same direction, their relative speed is the difference in their speeds.

  • Speed of the first train = 20 m/sec
  • Speed of the second train = 22 m/sec

Relative speed = 2220=222 - 20 = 2m/sec

  1. Calculate the total distance to be covered.

The total distance is the sum of the lengths of both trains.

  • Length of the first train = 200 m
  • Length of the second train = 100 m

Total distance = 200+100=300200 + 100 = 300m

  1. Calculate the time taken to cross each other.

Time = Total distanceRelative speed\frac{\text{Total distance}}{\text{Relative speed}}

  • Total distance = 300 m
  • Relative speed = 2 m/sec

Time = 3002=150\frac{300}{2} = 150 seconds

The correct answer is (C) 150 sec.



Importance for ADRE 2.0:

  1. Practical Application: Tests the ability to solve real-world problems involving relative speed, which is a common topic in competitive exams.
  2. Speed and Distance Concepts: Assesses understanding of basic physics concepts related to speed, distance, and time.
  3. Exam Preparation: Provides practice for similar questions that may appear in ADRE 2.0, enhancing problem-solving skills.

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