A train A which is 120 m long is running with velocity 20 m/s while train B which is 130 m long is running in opposite direction with velocity 30 m/s. What is the time taken by train B to cross the train A?

Options

A. 5 s
B. 25 s
C. 10 s
D. 100 s

Explanation

To solve the problem of how long it takes for train B to cross train A, we can follow these steps:

### Step 1: Identify the lengths of the trains
- Length of train A (L_A) = 120 m
- Length of train B (L_B) = 130 m

### Step 2: Identify the velocities of the trains
- Velocity of train A (V_A) = 20 m/s
- Velocity of train B (V_B) = 30 m/s

### Step 3: Calculate the relative speed
Since the trains are moving in opposite directions, we can find the relative speed (V_rel) by adding their speeds:
\[ V_{rel} = V_A + V_B = 20 \, \text{m/s} + 30 \, \text{m/s} = 50 \, \text{m/s} \]

### Step 4: Calculate the total distance to be covered
The total distance (D) that train B needs to cover to completely cross train A is the sum of their lengths:
\[ D = L_A + L_B = 120 \, \text{m} + 130 \, \text{m} = 250 \, \text{m} \]

### Step 5: Calculate the time taken to cross
Using the formula for time (T), which is distance divided by speed:
\[ T = \frac{D}{V_{rel}} = \frac{250 \, \text{m}}{50 \, \text{m/s}} = 5 \, \text{s} \]

### Final Answer:
The time taken by train B to cross train A is **5 seconds**.

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