A person seec a train passing over 1 km long bridge. The length of the train is half that of bridge. If the train clears the bridge in 2 minutes the speed of the train is -----

Options

A. 50 km/hr
B. 45 km/hr
C. 60 km/hr
D. 30 km/hr

Answer

To solve the problem step by step, we will follow the information provided in the question and the video transcript.

### Step 1: Understand the lengths involved
- The length of the bridge is given as 1 km.
- Convert the length of the bridge from kilometers to meters:
\[ 1 \text{ km} = 1000 \text{ meters} \]

**Hint:** Remember that 1 kilometer is equal to 1000 meters.

### Step 2: Calculate the length of the train
- The length of the train is half the length of the bridge:
\[ \text{Length of train} = \frac{1}{2} \times 1000 \text{ meters} = 500 \text{ meters} \]

**Hint:** To find half of a number, divide it by 2.

### Step 3: Calculate the total distance covered by the train
- The total distance covered by the train while passing over the bridge is the sum of the length of the train and the length of the bridge:
\[ \text{Total distance} = \text{Length of train} + \text{Length of bridge} = 500 \text{ meters} + 1000 \text{ meters} = 1500 \text{ meters} \]

**Hint:** When calculating total distance, simply add the lengths together.

### Step 4: Convert time from minutes to seconds
- The time taken for the train to clear the bridge is given as 2 minutes. Convert this to seconds:
\[ \text{Time} = 2 \text{ minutes} \times 60 \text{ seconds/minute} = 120 \text{ seconds} \]

**Hint:** To convert minutes to seconds, multiply by 60.

### Step 5: Calculate the speed of the train
- Use the formula for speed, which is distance divided by time:
\[ \text{Speed} = \frac{\text{Total distance}}{\text{Time}} = \frac{1500 \text{ meters}}{120 \text{ seconds}} = 12.5 \text{ meters/second} \]

**Hint:** The formula for speed is straightforward: Speed = Distance / Time.

### Step 6: Convert speed from meters per second to kilometers per hour
- To convert from meters per second to kilometers per hour, multiply by \(\frac{18}{5}\):
\[ \text{Speed in km/h} = 12.5 \text{ m/s} \times \frac{18}{5} = 12.5 \times 3.6 = 45 \text{ km/h} \]

**Hint:** Use the conversion factor \( \frac{18}{5} \) to convert m/s to km/h.

### Final Answer
The speed of the train is **45 kilometers per hour**.