How much time does a train. 50m long, moving at 68km/hour take to pass another train, 75m long, moving at 50km/hour in the same direction?

Options

A. A)5 seconds
B. B)10 seconds
C. C)20 seconds
D. D)25 seconds

Answer

To solve the problem of how much time a train takes to pass another train, we can follow these steps:

### Step 1: Determine the lengths of the trains
- Length of Train 1 (T1) = 50 meters
- Length of Train 2 (T2) = 75 meters

### Step 2: Calculate the total distance to be covered
When one train passes another, the total distance covered is the sum of the lengths of both trains:
- Total Distance = Length of T1 + Length of T2
- Total Distance = 50 m + 75 m = 125 m

### Step 3: Determine the speeds of the trains
- Speed of Train 1 (T1) = 68 km/h
- Speed of Train 2 (T2) = 50 km/h

### Step 4: Calculate the relative speed
Since both trains are moving in the same direction, the relative speed is the difference between their speeds:
- Relative Speed = Speed of T1 - Speed of T2
- Relative Speed = 68 km/h - 50 km/h = 18 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 = 18 km/h × (5/18) = 5 m/s

### Step 6: Calculate the time taken to pass
Using the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can substitute the values we have:
- Time = Total Distance / Relative Speed
- Time = 125 m / 5 m/s = 25 seconds

### Final Answer
The time taken for Train 1 to pass Train 2 is **25 seconds**.

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