Find the en by a train 150 m long running at a speed of 63 kmph to cross another train of length 100 m long running at ph in the same directionCorrect answer is '75'. Can you explain this answer?

Question

Answer

Approach to solve the problem:
To find the time taken by the train to cross another train, we need to calculate the relative speed between the two trains.

Given data:
- Length of first train (L1) = 150 m
- Speed of first train (S1) = 63 kmph
- Length of second train (L2) = 100 m
- Speed of second train (S2) = ? (to be found)

Formula:
Relative speed = (Speed of first train - Speed of second train)

Calculations:
- Speed of first train = 63 kmph = 63 * (5/18) m/s = 35/2 m/s
- Let the speed of the second train be S m/s
- Relative speed = (35/2 - S) m/s

Time taken to cross the second train:
Time = Distance / Relative speed
Time = (L1 + L2) / (35/2 - S)

Given data:
- L1 = 150 m
- L2 = 100 m

Substitute the values:
Time = (150 + 100) / (35/2 - S)
Time = 250 / (35/2 - S)
Time = 500 / (35 - 2S)

Given that the trains are moving in the same direction:
- Speed of first train (S1) = 35/2 m/s
- Speed of second train (S2) = S m/s

Relative speed formula:
Relative speed = 35/2 - S

Given that the relative speed is equal to the speed of the second train:
35/2 - S = S
35 = 2S + S
35 = 3S
S = 35/3
S = 11.67 m/s

Time taken to cross the second train:
Time = 500 / (35 - 2(11.67))
Time = 500 / (35 - 23.34)
Time = 500 / 11.66
Time ≈ 42.88 seconds

Answer:
Therefore, the time taken by the train to cross another train is approximately 43 seconds.

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