A train 180 m long moving at the speed of 20 m/sec.Over-takes a man moving at a speed of 10m/sec in the same direction .The traiin passes the man in:

Options

A. 6 sec
B. 9 sec
C. 18 sec
D. 27 sec

Answer

To find out how long it takes for a train to overtake a man moving in the same direction, we can follow these steps:

### Step 1: Identify the lengths and speeds
- Length of the train = 180 meters
- Speed of the train = 20 m/sec
- Speed of the man = 10 m/sec

### Step 2: Calculate the relative speed
Since both the train and the man are moving in the same direction, the relative speed of the train with respect to the man is calculated by subtracting the speed of the man from the speed of the train.

\[ \text{Relative Speed} = \text{Speed of Train} - \text{Speed of Man} \]
\[ \text{Relative Speed} = 20 \, \text{m/sec} - 10 \, \text{m/sec} = 10 \, \text{m/sec} \]

### Step 3: Calculate the time taken to overtake
To find the time it takes for the train to completely pass the man, we can use the formula:

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

In this case, the distance is the length of the train (180 meters), and the speed is the relative speed (10 m/sec).

\[ \text{Time} = \frac{180 \, \text{meters}}{10 \, \text{m/sec}} = 18 \, \text{seconds} \]

### Final Answer
The train passes the man in **18 seconds**.

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