How long will a train 130 m long travelling at 40 km an hour, take to pass a kilometre stone ?

Options

A. 12 sec
B. 11.7 sec
C. 11.2 sec
D. 11 sec

Answer

To solve the problem of how long a train 130 meters long traveling at 40 km/h takes to pass a kilometer stone, we can follow these steps:

### Step 1: Understand the Problem
We need to determine the time it takes for a train of length 130 meters to completely pass a stationary point (the kilometer stone).

### Step 2: Convert the Length of the Train to Kilometers
The length of the train is given in meters, and we need to convert it to kilometers since the speed is given in km/h.

- Length of the train = 130 meters
- Conversion: 1 kilometer = 1000 meters
- Therefore, \( \text{Length in kilometers} = \frac{130 \text{ meters}}{1000} = 0.13 \text{ kilometers} \)

### Step 3: Identify the Speed of the Train
The speed of the train is given as 40 km/h.

### Step 4: Use the Formula for Time
The formula to calculate time when distance and speed are known is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

### Step 5: Substitute the Values into the Formula
Now we can substitute the values we have into the formula:
- Distance = 0.13 kilometers
- Speed = 40 km/h

So,
\[ \text{Time} = \frac{0.13 \text{ km}}{40 \text{ km/h}} \]

### Step 6: Calculate the Time
Calculating the above expression gives:
\[ \text{Time} = \frac{0.13}{40} \text{ hours} \]

To convert hours into seconds, we multiply by 3600 (since 1 hour = 3600 seconds):
\[ \text{Time in seconds} = \left(\frac{0.13}{40}\right) \times 3600 \]

Calculating this:
\[ \text{Time in seconds} = \frac{0.13 \times 3600}{40} \]
\[ \text{Time in seconds} = \frac{468}{40} \]
\[ \text{Time in seconds} = 11.7 \text{ seconds} \]

### Final Answer
The time taken for the train to pass the kilometer stone is **11.7 seconds**.

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