Train Speed Calculation for Train A

Train A needs to cover the length of the train plus the length of the platform to completely cross it.

• Length of Train A = 260 m
• Length of Platform = 160 m
• Total distance covered by Train A = Length of Train A + Length of Platform = 260 m + 160 m = 420 m
• Time taken by Train A = 28 seconds
• Speed of Train A (\(S_A\)) = \(\frac{\text{Total Distance}}{\text{Time}}\) = \(\frac{420 \text{ m}}{28 \text{ s}}\) = 15 m/s

Train Speed Calculation for Train B

Train B needs to cover its own length to pass a stationary man.

• Length of Train B = 340 m
• Time taken by Train B = 20 seconds
• Speed of Train B (\(S_B\)) = \(\frac{\text{Length of Train B}}{\text{Time}}\) = \(\frac{340 \text{ m}}{20 \text{ s}}\) = 17 m/s

Identifying Faster and Slower Trains

Comparing the speeds:

• \(S_B\) = 17 m/s
• \(S_A\) = 15 m/s
• Since \(S_B > S_A\), Train B is the faster train and Train A is the slower train.

Calculating Overtaking Time

When two trains move in the same direction on parallel tracks, the faster train overtakes the slower train. The relative speed is the difference between their speeds.

• Relative Speed = Speed of Faster Train - Speed of Slower Train = \(S_B - S_A\)
• Relative Speed = 17 m/s - 15 m/s = 2 m/s
• Total distance required for the faster train (B) to completely overtake the slower train (A) is the sum of their lengths.
• Total Overtaking Distance = Length of Train A + Length of Train B = 260 m + 340 m = 600 m
• Time taken to overtake = \(\frac{\text{Total Overtaking Distance}}{\text{Relative Speed}}\)
• Time taken to overtake = \(\frac{600 \text{ m}}{2 \text{ m/s}}\) = 300 seconds

Therefore, the faster train takes 300 seconds to completely overtake the slower train.