Two trains A and B,186 m and 200 m long.are running at 64 km/h and 80 km/h, respectively on parallel tracks. If they are runningin the opposite directions, then how much time(in seconds) will a person sitting in the first train A take to cross the other train?

Options

A. `5.5`
B. 5
C. 6
D. `4.6`

Answer

To solve the problem of how much time a person sitting in train A takes to cross train B, we can follow these steps:

### Step 1: Understand the problem
We have two trains:
- Train A: Length = 186 m, Speed = 64 km/h
- Train B: Length = 200 m, Speed = 80 km/h

They are moving in opposite directions on parallel tracks.

### Step 2: Convert speeds from km/h to m/s
To work with the lengths in meters, we need to convert the speeds from kilometers per hour to meters per second using the conversion factor \( \frac{5}{18} \).

- Speed of Train A in m/s:
\[ 64 \text{ km/h} = 64 \times \frac{5}{18} = \frac{320}{18} \approx 17.78 \text{ m/s} \]

- Speed of Train B in m/s:
\[ 80 \text{ km/h} = 80 \times \frac{5}{18} = \frac{400}{18} \approx 22.22 \text{ m/s} \]

### Step 3: Calculate the relative speed
Since the trains are moving in opposite directions, we add their speeds to find the relative speed.

\[ \text{Relative Speed} = \text{Speed of Train A} + \text{Speed of Train B} \]
\[ \text{Relative Speed} = 17.78 \text{ m/s} + 22.22 \text{ m/s} = 40 \text{ m/s} \]

### Step 4: Determine the distance to be covered
When a person in Train A crosses Train B, the distance to be covered is equal to the length of Train B (since we are only considering the crossing of Train B).

\[ \text{Distance} = 200 \text{ m} \]

### Step 5: Use the formula to find time
We can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values we have:
\[ \text{Time} = \frac{200 \text{ m}}{40 \text{ m/s}} = 5 \text{ seconds} \]

### Conclusion
The time taken for a person sitting in Train A to cross Train B is **5 seconds**.

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