The length of Lucknow mail is 120 m and that of Punjab mail is 80 m These two trains are runing in the same direction with velocities of 40 km/h and 50 km/h respectively.The time taken by them to cross each other is:

Options

A. 8 s
B. 72 s
C. 11.5 s
D. 12.5 s

Answer

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

### Step 1: Determine the lengths of the trains
- Length of Lucknow mail = 120 m
- Length of Punjab mail = 80 m

### Step 2: Calculate the total distance to be covered when the trains cross each other
- Total distance = Length of Lucknow mail + Length of Punjab mail
- Total distance = 120 m + 80 m = 200 m

### Step 3: Determine the speeds of the trains
- Speed of Lucknow mail = 40 km/h
- Speed of Punjab mail = 50 km/h

### Step 4: Calculate the relative speed of the trains
- Since the trains are moving in the same direction, the relative speed is the difference in their speeds.
- Relative speed = Speed of Punjab mail - Speed of Lucknow mail
- Relative speed = 50 km/h - 40 km/h = 10 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: 1 km/h = 5/18 m/s.
- Relative speed in m/s = 10 km/h × (5/18) = (10 × 5) / 18 = 50 / 18 = 25 / 9 m/s ≈ 2.78 m/s

### Step 6: Use the formula for time
- We know that Time = Distance / Speed.
- Here, Distance = 200 m and Speed = 25/9 m/s.
- Time = 200 m / (25/9 m/s) = 200 m × (9/25) = 720/25 seconds = 28.8 seconds.

### Final Answer
The time taken by the two trains to cross each other is approximately 28.8 seconds.

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