Two trains one `60` m long and other is `80` m long are travelling in opposite direction with velocity `10` m/s and `25` m/s . The time of crossing is :

Options

A. `4` second
B. `5` second
C. `6` second
D. `3` second

Explanation

To solve the problem of two trains crossing each other, we can follow these steps:

### Step 1: Identify the lengths of the trains
- Train A is 60 meters long.
- Train B is 80 meters long.

### Step 2: Determine the velocities of the trains
- Velocity of Train A (vA) = 10 m/s
- Velocity of Train B (vB) = 25 m/s

### Step 3: Calculate the total distance to be covered when the trains cross each other
When two objects move towards each other, the total distance that needs to be covered for them to completely cross each other is the sum of their lengths:
- Total distance = Length of Train A + Length of Train B
- Total distance = 60 m + 80 m = 140 m

### Step 4: Calculate the relative velocity of the trains
Since the trains are moving in opposite directions, their velocities add up:
- Relative velocity (v_rel) = vA + vB
- v_rel = 10 m/s + 25 m/s = 35 m/s

### Step 5: Calculate the time taken to cross each other
The time taken to cross each other can be calculated using the formula:
\[ \text{Time} = \frac{\text{Total Distance}}{\text{Relative Velocity}} \]
Substituting the values:
\[ \text{Time} = \frac{140 \text{ m}}{35 \text{ m/s}} = 4 \text{ seconds} \]

### Final Answer
The time taken for the two trains to cross each other is **4 seconds**.

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