Question

A 250 m long train overtakes a man moving at a speed of 7 km/h (in same direction) in 36 seconds. How much time (in seconds) will it take this train to completely cross another 415 m long train, moving in the opposite direction at a speed of 82 km/h?

• A. 17
• B. 30
• C. 21
• D. 31

Answer 1

Answer:

C. 21

The train will take 21 seconds to completely cross the other train.

Step 1: Find the speed of the first train

• Distance covered: Length of the first train = 250 m

• Time taken: 36 seconds

• Relative speed formula: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$
  $\text{Relative Speed} = \frac{250}{36} \text{ m/s}$

• To convert this relative speed into km/h, multiply by $\frac{18}{5}$:
  $\text{Relative Speed} = \frac{250}{36} \times \frac{18}{5} = 25 \text{ km/h}$

• Since the train and the man are moving in the same direction:
  $\text{Relative Speed} = \text{Speed of Train 1} - \text{Speed of Man}$

• $25 = \text{Speed of Train 1} - 7$

  $\text{Speed of Train 1} = 25 + 7 = \mathbf{32 \text{ km/h}}$

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Step 2: Find the time taken to cross the second train

• Total distance to cover: Sum of both train lengths
  $\text{Total Distance} = 250 \text{ m} + 415 \text{ m} = \mathbf{665 \text{ m}}$

• Relative speed (opposite direction): Sum of both train speeds
  $\text{Relative Speed} = 32 \text{ km/h} + 82 \text{ km/h} = \mathbf{114 \text{ km/h}}$

• Convert the relative speed back to m/s:
  $\text{Relative Speed} = 114 \times \frac{5}{18} = \mathbf{\frac{95}{3} \text{ m/s}}$

• Calculate the final time:
  $\text{Time} = \frac{\text{Total Distance}}{\text{Relative Speed}}$

• $\text{Time} = 665 \div \frac{95}{3} = 665 \times \frac{3}{95} = 7 \times 3 = \mathbf{21 \text{ seconds}}$