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

Options

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

Answer

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

### Step 1: Identify the lengths and speeds of the trains
- Train 1 (T1) is 50 meters long and moves at a speed of 68 km/hr.
- Train 2 (T2) is 75 meters long and moves at a speed of 50 km/hr.

### Step 2: Calculate the total distance to be covered
The total distance that needs to be covered when one train passes the other is the sum of their lengths.
\[ \text{Total Distance} = L1 + L2 = 50 \text{ m} + 75 \text{ m} = 125 \text{ m} \]

### Step 3: Calculate the relative speed
Since both trains are moving in the same direction, we need to find the relative speed. The relative speed is the difference between the speeds of the two trains.
\[ \text{Relative Speed} = V1 - V2 = 68 \text{ km/hr} - 50 \text{ km/hr} = 18 \text{ km/hr} \]

### Step 4: Convert the relative speed to meters per second
To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \).
\[ \text{Relative Speed in m/s} = 18 \text{ km/hr} \times \frac{5}{18} = 5 \text{ m/s} \]

### Step 5: Calculate the time taken to pass each other
Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can substitute the total distance and the relative speed:
\[ \text{Time} = \frac{125 \text{ m}}{5 \text{ m/s}} = 25 \text{ seconds} \]

### Final Answer
The time taken for the first train to pass the second train is **25 seconds**.

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