Problem On Trains

Step 1: Understanding the relationship.
Let the length of the train be meters and the speed of the train be meters per second. When the train passes a standing man, it covers its own length, , in 6 seconds. Hence, the speed of the train can be calculated as: When the train passes a platform of length 210 m, it covers a distance equal to the length of the train plus the length of the platform, i.e., meters, in 16 seconds. So, the speed of the train can also be written as: Step 2: Set up the equations.
From the two equations for speed , we have: Step 3: Solve for .
Cross-multiply to solve for : Expanding the equation: Simplifying: Step 4: Calculate the speed of the train.
Now, substitute into the equation to find the speed: Step 5: Conclusion.
The length of the train is 126 meters and the speed is 21 m/s. Thus, the correct answer is (1) 126 m, 21 m/s.