A train 120 metres long travels at 60 km/hr. A man is running at 6 km/h in the same direction in which the train is going. The train will cross man in:

Options

A. 6 seconds
B. 7 seconds
C. 6 seconds
D. 8 seconds

Answer

To solve the problem of how long it takes for a train to cross a man running in the same direction, we can follow these steps:

### Step 1: Identify the lengths and speeds
- Length of the train = 120 meters
- Speed of the train = 60 km/h
- Speed of the man = 6 km/h

### Step 2: Calculate the relative speed
Since both the train and the man are moving in the same direction, we need to find the relative speed of the train with respect to the man. The formula for relative speed when two objects are moving in the same direction is:

\[ \text{Relative Speed} = \text{Speed of Train} - \text{Speed of Man} \]

Substituting the values:

\[ \text{Relative Speed} = 60 \text{ km/h} - 6 \text{ km/h} = 54 \text{ km/h} \]

### Step 3: Convert the relative speed to meters per second
To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \):

\[ \text{Relative Speed in m/s} = 54 \text{ km/h} \times \frac{5}{18} \]

Calculating this gives:

\[ \text{Relative Speed in m/s} = 54 \times \frac{5}{18} = 15 \text{ m/s} \]

### Step 4: Calculate the time taken to cross the man
The time taken to cross an object can be calculated using the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

In this case, the distance is the length of the train (120 meters) and the speed is the relative speed (15 m/s):

\[ \text{Time} = \frac{120 \text{ meters}}{15 \text{ m/s}} = 8 \text{ seconds} \]

### Final Answer
The train will cross the man in **8 seconds**.

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