The time taken by a train 180 m long, travelling at 42 kmph, in pasing a person walking in the

same direction at 6 kmph, will be

To solve the problem, we need to determine how long the train will take to pass the person walking in the same direction. The length of the train is given as 180 meters, and both the train and the person are moving in the same direction.

### Step-by-step solution:

1. **Speed of the train:**
   The train's speed is 42 km/h.

2. **Speed of the person:**
   The person's speed is 6 km/h.

3. **Relative speed (since they are moving in the same direction):**
   When two objects move in the same direction, the relative speed is the difference between their speeds.
   \[
   \text{Relative speed} = 42 - 6 = 36 \text{ km/h}
   \]

4. **Convert relative speed to meters per second:**
   We need to convert the speed from km/h to m/s using the conversion factor \( 1 \, \text{km/h} = \frac{5}{18} \, \text{m/s} \).
   \[
   \text{Relative speed} = 36 \times \frac{5}{18} = 10 \text{ m/s}
   \]

5. **Time taken to pass the person:**
   The train needs to cover its own length of 180 meters. The time taken to pass the person can be calculated using the formula:
   \[
   \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{180}{10} = 18 \, \text{seconds}
   \]

### Conclusion:
The train will take **18 seconds** to pass the person.

Would you like more details or have any questions? 

Here are 5 related questions for further practice:

1. If the person was walking at 4 km/h, what would the time taken be?
2. How would the time change if the train's speed was increased to 54 km/h?
3. What if the person was walking in the opposite direction? How would you calculate the time?
4. If the train was 240 meters long, what would the time be with the same speeds?
5. What if there were two people walking side by side at different speeds? How would you handle that?

**Tip:** When calculating time, always make sure the units for distance and speed are consistent.

The time taken by a train 180 m long, travelling at 42 kmph, in passing a person walking in the same direction at 6 kmph, will be

Find out how long it takes for a train 180 meters long, traveling at 42 km/h, to pass a person walking at 6 km/h. This problem uses concepts of relative speed, unit conversion, and distance-time calculations, suitable for students in Grades 6-8.

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