Two trains of length 100m are running on parallel tracks . One overtake the other I in 20s when they are moving in the same direction and crosses the other in 10s when they are in opposite direction . The velocities of the train are

Calculating Relative Speeds

When the trains are moving in the same direction, the relative speed is the difference of their speeds:

Relative Speed (Same Direction) = v_A - v_B

When they are moving in opposite directions, the relative speed is the sum of their speeds:

Relative Speed (Opposite Direction) = v_A + v_B

Setting Up Equations

Now, let's set up the equations based on the time taken to overtake:

1. Overtaking in the Same Direction

When Train A overtakes Train B in 20 seconds, the distance covered is equal to the length of Train A plus the length of Train B:

Distance = Length of Train A + Length of Train B = 100m + 100m = 200m

Using the formula: Distance = Speed × Time, we have:

200 = (v_A - v_B) × 20

This simplifies to:

v_A - v_B = 10 (Equation 1)

2. Crossing in the Opposite Direction

When they cross each other in 10 seconds, the distance remains the same:

200 = (v_A + v_B) × 10

This simplifies to:

v_A + v_B = 20 (Equation 2)

Solving the Equations

Now we have a system of two equations:

• v_A - v_B = 10 (Equation 1)
• v_A + v_B = 20 (Equation 2)

To solve for v_A and v_B, we can add both equations:

(v_A - v_B) + (v_A + v_B) = 10 + 20

This simplifies to:

2v_A = 30

Thus, we find:

v_A = 15 m/s

Now, substituting v_A back into Equation 1 to find v_B:

15 - v_B = 10

Solving for v_B gives:

v_B = 5 m/s

Final Results

In conclusion, the velocities of the trains are:

• Train A: 15 m/s
• Train B: 5 m/s

This analysis shows how we can use relative speed and time to determine the velocities of moving objects. If you have any further questions or need clarification on any part of this process, feel free to ask!