The length of the two trains are 60 m and 90 m. They are running at the speed of 58 km/hr and 50 km/hr respectively on parallel tracks in opposite direction . In how many seconds will they pass each other .?

Options

A. 10
B. 8
C. 5
D. 3

Explanation

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

### Step 1: Identify the lengths of the trains
The lengths of the two trains are given as:
- Train 1: 60 meters
- Train 2: 90 meters

### Step 2: Calculate the total distance to be covered when the trains pass each other
When two trains pass each other, the distance covered is the sum of their lengths:
\[ \text{Total Distance} = \text{Length of Train 1} + \text{Length of Train 2} \]
\[ \text{Total Distance} = 60 \, \text{m} + 90 \, \text{m} = 150 \, \text{m} \]

### Step 3: Determine the speeds of the trains
The speeds of the trains are given as:
- Speed of Train 1: 58 km/hr
- Speed of Train 2: 50 km/hr

### Step 4: Calculate the relative speed of the trains
Since the trains are moving in opposite directions, their speeds will be added to find the relative speed:
\[ \text{Relative Speed} = \text{Speed of Train 1} + \text{Speed of Train 2} \]
\[ \text{Relative Speed} = 58 \, \text{km/hr} + 50 \, \text{km/hr} = 108 \, \text{km/hr} \]

### Step 5: Convert the relative speed from km/hr to m/s
To convert km/hr to m/s, we multiply by \(\frac{5}{18}\):
\[ \text{Relative Speed in m/s} = 108 \times \frac{5}{18} = 30 \, \text{m/s} \]

### Step 6: Calculate the time taken to pass each other
Using the formula for time, which is distance divided by speed:
\[ \text{Time} = \frac{\text{Total Distance}}{\text{Relative Speed}} \]
\[ \text{Time} = \frac{150 \, \text{m}}{30 \, \text{m/s}} = 5 \, \text{seconds} \]

### Final Answer
The time taken for the two trains to pass each other is **5 seconds**.

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