A train 120 m long is running with a speed of 64 km/h . What time is taken for it to pass a man who is running at 4 km/h in the same direction in which the train is moving ?

Answer

To solve the problem step by step, we need to find the time taken by a train to pass a man running in the same direction. Here’s how we can do it:

### Step 1: Understand the Problem
We have a train that is 120 meters long and is moving at a speed of 64 km/h. There is a man running at a speed of 4 km/h in the same direction as the train. We need to find out how long it takes for the train to completely pass the man.

### Step 2: Convert Speeds from km/h to m/s
To make calculations easier, we will convert the speeds from kilometers per hour (km/h) to meters per second (m/s). The conversion factor is:
1 km/h = (1000 m) / (3600 s) = 1/3.6 m/s.

- Speed of the train in m/s:
\[ 64 \text{ km/h} = \frac{64}{3.6} \approx 17.78 \text{ m/s} \]

- Speed of the man in m/s:
\[ 4 \text{ km/h} = \frac{4}{3.6} \approx 1.11 \text{ m/s} \]

### Step 3: Calculate the Relative Speed
Since both the train and the man are moving in the same direction, we need to find the relative speed of the train with respect to the man. This is done by subtracting the speed of the man from the speed of the train.

\[ \text{Relative Speed} = \text{Speed of Train} - \text{Speed of Man} \]
\[ \text{Relative Speed} = 17.78 \text{ m/s} - 1.11 \text{ m/s} = 16.67 \text{ m/s} \]

### Step 4: Calculate the Time Taken to Pass the Man
The time taken to pass the man can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Here, the distance is the length of the train (120 m) and the speed is the relative speed we just calculated.

\[ \text{Time} = \frac{120 \text{ m}}{16.67 \text{ m/s}} \approx 7.20 \text{ seconds} \]

### Step 5: Conclusion
The time taken for the train to pass the man is approximately **7.20 seconds**.

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