A train A of length 180 m, running by 72 km/h to cross the another train B which is running in the opposite direction to speed of 108 km/h and length is 120 m, in how much time?

Options

A. a. 23s
B. b. 12s
C. c. 6s
D. d. 30s

Answer

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

### Step 1: Convert the speeds from km/h to m/s
- Train A's speed = 72 km/h
- Train B's speed = 108 km/h

To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \).

\[ \text{Speed of Train A in m/s} = 72 \times \frac{5}{18} = 20 \text{ m/s} \]

\[ \text{Speed of Train B in m/s} = 108 \times \frac{5}{18} = 30 \text{ m/s} \]

### Step 2: Calculate the relative speed
Since the trains are moving in opposite directions, we add their speeds to find the relative speed.

\[ \text{Relative Speed} = \text{Speed of Train A} + \text{Speed of Train B} = 20 + 30 = 50 \text{ m/s} \]

### Step 3: Calculate the total distance to be covered
To cross each other, the total distance is the sum of their lengths.

- Length of Train A = 180 m
- Length of Train B = 120 m

\[ \text{Total Distance} = \text{Length of Train A} + \text{Length of Train B} = 180 + 120 = 300 \text{ m} \]

### Step 4: Calculate the time taken to cross
Using the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \):

\[ \text{Time} = \frac{\text{Total Distance}}{\text{Relative Speed}} = \frac{300}{50} = 6 \text{ seconds} \]

### Final Answer
The time taken for Train A to cross Train B is **6 seconds**.

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