A train crosses a man standing at a station in 6 seconds while it crosses another man who is walking in the same direction as that of train with speed 's' m/s in 7 seconds. If the length of the train is 96 meters, then find the value of s.

Let's solve this step by step.

### Step 1: Determine the speed of the train
When the train crosses a man standing still, the distance covered by the train is equal to its length, and the time taken is given. 

- Length of the train, \( L = 96 \) meters
- Time taken to cross the standing man, \( t_1 = 6 \) seconds

The speed of the train \( v \) (in meters per second) can be calculated using the formula:
\[
v = \frac{L}{t_1}
\]
\[
v = \frac{96}{6} = 16 \, \text{m/s}
\]

### Step 2: Determine the speed relative to the walking man
When the train crosses a man walking in the same direction, the relative speed between the train and the man comes into play. The relative speed will be the speed of the train minus the speed of the man \( s \).

The time taken to cross the walking man is given as \( t_2 = 7 \) seconds. 

The relative speed can be calculated using the formula:
\[
v - s = \frac{L}{t_2}
\]
\[
16 - s = \frac{96}{7} \approx 13.71 \, \text{m/s}
\]

### Step 3: Solve for \( s \)
Now, solve for the speed of the man \( s \):
\[
s = 16 - 13.71 = 2.29 \, \text{m/s}
\]

### Final Answer

The speed of the man \( s \) is approximately **2.29 m/s**.

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Would you like further details or have any questions?

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**Here are 8 follow-up questions:**

1. What would the speed of the man be if the train crossed him in 8 seconds instead of 7?
2. How would the value of \( s \) change if the length of the train were different?
3. If the man were walking in the opposite direction to the train, how would the crossing time be affected?
4. What is the relative speed if the man were stationary and the train crosses him in 8 seconds?
5. How long would it take for the train to cross the man if he increased his speed to 4 m/s?
6. Can you calculate the time taken by the train to cross a platform of length 120 meters?
7. What is the importance of the direction of the man’s motion in this scenario?
8. How would the problem change if the train's speed was not constant?

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**Tip:** Always pay attention to the relative motion between objects when calculating speeds, especially when they are moving in the same or opposite directions.

Learn how to calculate the speed of a man walking as a train crosses him with a detailed step-by-step solution. This problem covers speed, distance, and time calculations, as well as relative motion concepts. Suitable for high school students.

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