Two trains A and B 100 m and 60 m long are moving in opposite direction on parallel tracks. The velocity of the shorter train is 3 times that of the longer one. If the trains take 4s to cross each other, the velocities of the trains are

Explanation

To solve the problem, we need to find the velocities of two trains A and B that are moving in opposite directions. Here are the steps to find the solution:

### Step 1: Define the Variables
Let the velocity of train A (the longer train) be \( v \) m/s. Since train B (the shorter train) is moving at a velocity that is 3 times that of train A, we can express its velocity as \( 3v \) m/s.

### Step 2: Calculate the Total Distance
The total distance that needs to be covered when the two trains cross each other is the sum of their lengths. Train A is 100 m long and train B is 60 m long. Therefore, the total distance \( D \) is:
\[ D = \text{Length of Train A} + \text{Length of Train B} = 100 \, \text{m} + 60 \, \text{m} = 160 \, \text{m} \]

### Step 3: Determine the Relative Velocity
Since the trains are moving in opposite directions, their relative velocity \( V_{relative} \) when they cross each other is the sum of their individual velocities:
\[ V_{relative} = v + 3v = 4v \]

### Step 4: Use the Time to Cross Each Other
We know that the time taken to cross each other is 4 seconds. We can use the formula:
\[ \text{Distance} = \text{Relative Velocity} \times \text{Time} \]
Substituting the values we have:
\[ 160 \, \text{m} = (4v) \times 4 \, \text{s} \]

### Step 5: Solve for \( v \)
Now, we can solve for \( v \):
\[ 160 = 16v \]
\[ v = \frac{160}{16} = 10 \, \text{m/s} \]

### Step 6: Calculate the Velocity of Train B
Now that we have the velocity of train A, we can find the velocity of train B:
\[ \text{Velocity of Train B} = 3v = 3 \times 10 = 30 \, \text{m/s} \]

### Final Answer
The velocities of the trains are:
- Velocity of Train A: \( 10 \, \text{m/s} \)
- Velocity of Train B: \( 30 \, \text{m/s} \)

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