A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger? `3. 6\ s e c` b. `36\ s e c` c. `18\ s e c` d. `72\ s e c`

Options

A. 3.6 s
B. 18 s
C. 36 s
D. 72 s

Answer

To solve the problem of how long it will take for the train to pass the jogger, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Speeds of the Jogger and the Train:**
- Speed of the jogger = 9 km/h
- Speed of the train = 45 km/h

2. **Convert Speeds from km/h to m/s:**
- To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \).
- Speed of the jogger in m/s:
\[ 9 \text{ km/h} = 9 \times \frac{5}{18} = 2.5 \text{ m/s} \]
- Speed of the train in m/s:
\[ 45 \text{ km/h} = 45 \times \frac{5}{18} = 12.5 \text{ m/s} \]

3. **Calculate the Relative Speed of the Train with Respect to the Jogger:**
- Since both are moving in the same direction, the relative speed of the train with respect to the jogger is:
\[ \text{Relative Speed} = \text{Speed of Train} - \text{Speed of Jogger} = 12.5 \text{ m/s} - 2.5 \text{ m/s} = 10 \text{ m/s} \]

4. **Determine the Total Distance to be Covered by the Train:**
- The train needs to cover the distance between the jogger and the front of the train plus the length of the train itself.
- Distance ahead of the engine = 240 m
- Length of the train = 120 m
- Total distance to be covered:
\[ \text{Total Distance} = 240 \text{ m} + 120 \text{ m} = 360 \text{ m} \]

5. **Calculate the Time Taken for the Train to Pass the Jogger:**
- Time is calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{360 \text{ m}}{10 \text{ m/s}} = 36 \text{ seconds} \]

### Final Answer:
The time taken for the train to pass the jogger is **36 seconds**.