A train 110 metre long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6kmph in the direction opposite to that in which the train is going?

Options

A. 5 seconds
B. 6 seconds
C. 7 seconds
D. 10 seconds

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the problem
We have a train that is 110 meters long and is moving at a speed of 60 km/h. There is a man running in the opposite direction at a speed of 6 km/h. We need to find out how long it takes for the train to completely pass the man.

### Step 2: Calculate the relative speed
Since the train and the man are moving in opposite directions, we will add their speeds to find the relative speed.

- Speed of the train = 60 km/h
- Speed of the man = 6 km/h

Relative speed = Speed of the train + Speed of the man
Relative speed = 60 km/h + 6 km/h = 66 km/h

### Step 3: Convert the relative speed from km/h to m/s
To convert km/h to m/s, we use the conversion factor:
1 km/h = (1000 meters / 3600 seconds) = 5/18 m/s.

Now, we convert 66 km/h to m/s:

Relative speed in m/s = 66 * (5/18) = 66 * (5/18) = 18.33 m/s (approximately).

### Step 4: Use the formula to find time
We know that:
Distance = Speed × Time

We need to find the time it takes for the train to pass the man. The distance to be covered is the length of the train, which is 110 meters.

Rearranging the formula to find time:
Time = Distance / Speed

Substituting the values:
Time = 110 meters / 18.33 m/s

### Step 5: Calculate the time
Now we perform the calculation:
Time ≈ 110 / 18.33 ≈ 6 seconds (approximately).

### Final Answer
The train will take approximately **6 seconds** to pass the man.

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