Two train are of lengths 150 metre and 250 metre respectively. Trains are running at the speed of 45 km/hr and 65 km/hr respectively in same direction What will be the time taken by second train to cross the first train ?

Options

A. 1 min 15 sec
B. 1 min 12 sec
C. 1 min 30 sec
D. 2 min 15 sec

Answer

To solve the problem of how long it will take for the second train to cross the first train, we can follow these steps:

### Step 1: Identify the lengths of the trains
- Length of Train A = 150 meters
- Length of Train B = 250 meters

### Step 2: Calculate the total distance to be covered
- Total distance = Length of Train A + Length of Train B
- Total distance = 150 meters + 250 meters = 400 meters

### Step 3: Determine the speeds of the trains
- Speed of Train A = 45 km/hr
- Speed of Train B = 65 km/hr

### Step 4: Calculate the relative speed of the two trains
Since both trains are moving in the same direction, we find the relative speed by subtracting the speed of Train A from the speed of Train B.
- Relative speed = Speed of Train B - Speed of Train A
- Relative speed = 65 km/hr - 45 km/hr = 20 km/hr

### Step 5: Convert the relative speed from km/hr to m/s
To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \).
- Relative speed in m/s = 20 km/hr × \( \frac{5}{18} \)
- Relative speed in m/s = \( \frac{100}{18} \) m/s ≈ 5.56 m/s

### Step 6: Calculate the time taken to cross the first train
Using the formula for time, which is distance divided by speed:
- Time = Total distance / Relative speed
- Time = 400 meters / \( \frac{100}{18} \) m/s
- Time = 400 × \( \frac{18}{100} \) seconds
- Time = 72 seconds

### Step 7: Convert time into minutes and seconds
- 72 seconds can be expressed as 1 minute and 12 seconds.

### Final Answer
The time taken by the second train to cross the first train is **1 minute and 12 seconds**.

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