A 200 metre long train crosses a 300 metre long bridge in 30 seconds what time will it take to cross a man standing in the middle of 150 metre long platform? (In both the cases the speed is same

To solve this problem, we need to first calculate the speed of the train based on the given information about the train crossing the bridge.

### Step 1: Calculate the speed of the train
- The length of the train is \(200 \, \text{metres}\).
- The length of the bridge is \(300 \, \text{metres}\).
- The train crosses the entire bridge in \(30 \, \text{seconds}\).

When the train crosses the bridge, it covers a total distance equal to the sum of the train's length and the bridge's length:
\[
\text{Total distance} = 200 \, \text{m} + 300 \, \text{m} = 500 \, \text{metres}
\]
The speed of the train is:
\[
\text{Speed} = \frac{\text{Total distance}}{\text{Time}} = \frac{500 \, \text{metres}}{30 \, \text{seconds}} = \frac{500}{30} \, \text{m/s} \approx 16.67 \, \text{m/s}
\]

### Step 2: Time taken to cross the man on the platform
The length of the platform is \(150 \, \text{metres}\), but since the man is standing in the middle, we are only interested in the train crossing the man. To cross the man, the train only needs to cover its own length, which is \(200 \, \text{metres}\).

The time taken to cross the man is:
\[
\text{Time} = \frac{\text{Length of the train}}{\text{Speed}} = \frac{200 \, \text{metres}}{16.67 \, \text{m/s}} \approx 12 \, \text{seconds}
\]

Thus, the train will take approximately **12 seconds** to cross the man standing on the platform.

Would you like any further details or clarifications?

Here are 5 related questions to expand your understanding:
1. How would the time change if the train's speed increased by 20%?
2. What would be the time taken if the man was standing at the edge of the platform?
3. How long would it take for the train to cross a tunnel of 500 meters?
4. How would the scenario change if the train had to decelerate while crossing the bridge?
5. How can you calculate the train's average speed if it accelerates halfway through the bridge?

**Tip**: Remember that when a train crosses an object (like a bridge or person), it covers not only the object's length but also its own length.

A 200 metre long train crosses a 300 metre long bridge in 30 seconds. What time will it take to cross a man standing in the middle of a 150 metre long platform? (In both the cases the speed is same).

Learn how to calculate the time it takes for a 200 metre long train to cross a man standing on a 150 metre platform. This problem involves key concepts of speed, distance, and time, and is suitable for students in Grades 6-8.

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