A train is running at a speed of 45 km/hr and a man is walking at a speed of 5 km/hr in the opposite direction. If the train crosses the man in 18 seconds, then its length is

Options

A. 200 m
B. 220 m
C. 180 m
D. 250 m

Answer

To solve the problem, we need to find the length of the train based on the given speeds and the time taken to cross the man. Here’s the step-by-step solution:

### Step 1: Understand the relative speed
Since the train and the man are moving in opposite directions, we can find the relative speed by adding their speeds together.

- Speed of the train = 45 km/hr
- Speed of the man = 5 km/hr

**Relative Speed = Speed of Train + Speed of Man**
\[ \text{Relative Speed} = 45 \text{ km/hr} + 5 \text{ km/hr} = 50 \text{ km/hr} \]

### Step 2: Convert the relative speed to meters per second
To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \).

\[ \text{Relative Speed in m/s} = 50 \text{ km/hr} \times \frac{5}{18} = \frac{250}{18} \approx 13.89 \text{ m/s} \]

### Step 3: Use the time to find the length of the train
The length of the train can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Here, the distance is the length of the train, the speed is the relative speed we just calculated, and the time is given as 18 seconds.

\[ \text{Length of the Train} = \text{Relative Speed} \times \text{Time} \]
\[ \text{Length of the Train} = 13.89 \text{ m/s} \times 18 \text{ s} \approx 250 \text{ meters} \]

### Conclusion
The length of the train is approximately **250 meters**.

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