The speed of a train is 72km/hr and its length is 200 metre. What will be the time (in minutes) taken by the train to cross a pole?

Options

A. `(1)/(6)`
B. `(3)/(5)`
C. 5
D. 10

Answer

To solve the problem of how long it takes for a train to cross a pole, we can follow these steps:

### Step 1: Understand the problem
We need to find the time taken by a train to cross a pole. The length of the train is given, and we know its speed.

### Step 2: Identify the given values
- Speed of the train = 72 km/hr
- Length of the train = 200 meters

### Step 3: Convert speed from km/hr to m/s
To use the formula for time, we need to convert the speed from kilometers per hour to meters per second. The conversion factor is:
\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]
So, we convert 72 km/hr to m/s:
\[ \text{Speed in m/s} = 72 \times \frac{5}{18} \]

### Step 4: Calculate the speed in m/s
Calculating the speed:
\[ 72 \times \frac{5}{18} = 72 \div 18 \times 5 = 4 \times 5 = 20 \text{ m/s} \]

### Step 5: Use the formula for time
The formula for time is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Here, the distance is the length of the train (200 meters) and the speed is 20 m/s. So we can substitute these values into the formula:
\[ \text{Time} = \frac{200 \text{ meters}}{20 \text{ m/s}} \]

### Step 6: Calculate the time in seconds
Calculating the time:
\[ \text{Time} = \frac{200}{20} = 10 \text{ seconds} \]

### Step 7: Convert time from seconds to minutes
To convert seconds to minutes, we divide by 60:
\[ \text{Time in minutes} = \frac{10 \text{ seconds}}{60} = \frac{1}{6} \text{ minutes} \]

### Final Answer
The time taken by the train to cross the pole is \(\frac{1}{6}\) minutes.

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