Two trains 85 m and 155 m long, runat the speeds of 62 km/h and 82 km/h respectively, in opposite directions on parallel tracks. The time which they take to cross each other is:

Options

A. 4 seconds
B. 5 seconds
C. 6 seconds
D. 8 seconds

Answer

To solve the problem of how long it takes for two trains to cross each other, we can follow these steps:

### Step 1: Identify the lengths of the trains
- Train 1 length = 85 meters
- Train 2 length = 155 meters

### Step 2: Calculate the total distance to be covered
The total distance the trains need to cover to completely cross each other is the sum of their lengths:
\[ \text{Total Distance} = \text{Length of Train 1} + \text{Length of Train 2} = 85 \, \text{m} + 155 \, \text{m} = 240 \, \text{m} \]

### Step 3: Identify the speeds of the trains
- Speed of Train 1 = 62 km/h
- Speed of Train 2 = 82 km/h

### Step 4: Calculate the relative speed of the trains
Since the trains are moving in opposite directions, we add their speeds:
\[ \text{Relative Speed} = \text{Speed of Train 1} + \text{Speed of Train 2} = 62 \, \text{km/h} + 82 \, \text{km/h} = 144 \, \text{km/h} \]

### Step 5: Convert the relative speed from km/h to m/s
To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \):
\[ \text{Relative Speed in m/s} = 144 \, \text{km/h} \times \frac{5}{18} = 40 \, \text{m/s} \]

### Step 6: Calculate the time taken to cross each other
Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can substitute the values we have:
\[ \text{Time} = \frac{240 \, \text{m}}{40 \, \text{m/s}} = 6 \, \text{seconds} \]

### Final Answer
The time taken for the two trains to cross each other is **6 seconds**.

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