The number of seconds taken by a 500 m. long train with speed 63 km per hour to cross a man walking at 3 km per hour in the same direction is

Options

A. 20
B. 25
C. 30
D. 35

Answer

To solve the problem step by step, we need to find out how long it takes for a 500 m long train traveling at 63 km/h to cross a man walking at 3 km/h in the same direction.

### Step 1: Understand the problem
We have a train and a man both moving in the same direction. The train is 500 meters long, and we need to calculate the time it takes for the train to completely pass the man.

### Step 2: Convert speeds from km/h to m/s
To work with consistent units, we need to convert the speeds from kilometers per hour (km/h) to meters per second (m/s). The conversion factor is:
\[ 1 \text{ km/h} = \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{5}{18} \text{ m/s} \]

- Speed of the train:
\[ 63 \text{ km/h} = 63 \times \frac{5}{18} = \frac{315}{18} = 17.5 \text{ m/s} \]

- Speed of the man:
\[ 3 \text{ km/h} = 3 \times \frac{5}{18} = \frac{15}{18} = 0.8333 \text{ m/s} \]

### Step 3: Calculate the relative speed
Since both the train and the man are moving in the same direction, we find the relative speed by subtracting the speed of the man from the speed of the train:
\[ \text{Relative Speed} = \text{Speed of Train} - \text{Speed of Man} = 17.5 \text{ m/s} - 0.8333 \text{ m/s} = 16.6667 \text{ m/s} \]

### Step 4: Calculate the time taken to cross the man
The time taken to cross the man can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Here, the distance is the length of the train (500 m) and the speed is the relative speed (16.6667 m/s):
\[ \text{Time} = \frac{500 \text{ m}}{16.6667 \text{ m/s}} \approx 30 \text{ seconds} \]

### Final Answer
The train takes approximately **30 seconds** to cross the man.

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