A train 150 m long is running at a speed of 68 km/hr. In what time (in seconds) will it completely pass a man who is running at 8 km/hr in the same direction as the train?

Introduction / Context:
This problem is a classic relative speed question in which a train overtakes a man running in the same direction. The key idea is that the effective speed at which the train approaches the man is the difference of their speeds, not the individual speeds. The time taken to overtake depends on this relative speed and the train's length.

Given Data / Assumptions:
- Length of the train = 150 m.
- Speed of the train = 68 km/hr.
- Speed of the man = 8 km/hr.
- Both are moving in the same direction along a straight path.
- We must find the time in seconds for the train to completely pass the man.

Concept / Approach:
When two objects move in the same direction, their relative speed equals the difference of their speeds. The train must travel a distance equal to its own length relative to the man in order to overtake him fully. Once we find the relative speed in m/s, we apply time = distance / relative speed using the train's length as the distance.

Step-by-Step Solution:
Step 1: Compute the relative speed: 68 km/hr (train) minus 8 km/hr (man) = 60 km/hr.Step 2: Convert 60 km/hr to m/s using the factor 5 / 18.Step 3: Relative speed in m/s = 60 * (5 / 18) = 300 / 18 = 50 / 3 m/s.Step 4: Distance for overtaking = length of the train = 150 m.Step 5: Use time = distance / speed: time = 150 / (50 / 3) seconds.Step 6: Simplify: 150 / (50 / 3) = 150 * 3 / 50 = 450 / 50 = 9 seconds.Step 7: Hence, the train takes 9 seconds to completely pass the man.

Verification / Alternative check:
We can do a quick sense check. Relative speed of 60 km/hr is about 16.67 m/s. A 150 m train at 16.67 m/s would need about 150 / 16.67 ≈ 9 seconds to overtake fully, which aligns perfectly with the detailed calculation. This confirms both the method and the answer.

Why Other Options Are Wrong:
8 or 8.5 seconds would require a slightly higher relative speed than 60 km/hr. 9.5 seconds implies a slower relative speed; if substituted back, it would not match the given absolute speeds. 10 seconds similarly leads to a relative speed smaller than 60 km/hr, contradicting the given values. Only 9 seconds fits the relative speed calculation exactly.

Common Pitfalls:
A common mistake is to add the speeds instead of subtracting them, which is only valid when objects move in opposite directions. Another frequent error is using the sum of lengths of both objects; here, only the train has length, so we use 150 m, not more. Forgetting to convert from km/hr to m/s also leads to incorrect time values.

Final Answer:
The 150 m long train will pass the man completely in 9 seconds.