A train 125 m long is running at 50 km/hr. In what time will it pass a man, running at 5 km/hr in the same direction in which the train is going?

Appeared in: NORCET 3 - 2022 (Shift-2)

Explanation

The core concept is relative speed. Since the train and the man are moving in the same direction, the relative speed is the difference between their speeds: 50 km/hr - 5 km/hr = 45 km/hr.
For calculations involving time in seconds and distance in meters, the speed must be converted from km/hr to m/s by multiplying by 5/18. So, 45 km/hr becomes 45 * (5/18) = 12.5 m/s.
The distance the train needs to cover to pass the man is its own length, which is 125 meters.
Using the formula Time = Distance / Speed, the time taken is 125 meters / 12.5 m/s = 10 seconds.

Option B: This result would be obtained from an incorrect calculation of relative speed or a mistake in the final division.
Option C: This is an incorrect answer arising from miscalculation. A common mistake is incorrectly converting units or using the wrong relative speed.
Option D: This answer is incorrect and likely stems from a calculation error, possibly in the conversion from km/hr to m/s or in the final division.

Visual 1: Infographic: A diagram illustrating the concept of relative speed, showing two objects moving in the same direction. The relative speed is shown as the difference between the two individual speeds, which is the effective speed at which one object overtakes the other.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Relative Speed as background academic context rather than a clinical decision trigger.
This question tests quantitative aptitude and problem-solving skills, which are essential components of the general intelligence and reasoning sections of many nursing and other competitive examinations.
While not directly related to clinical practice, the ability to perform accurate calculations quickly is a valuable skill for nurses, especially in areas like medication dosage calculation and IV drip rate monitoring.
What if the man was running in the opposite direction? The relative speed would be the sum of their speeds (50 + 5 = 55 km/hr). The time to pass would then be 125 / (55 * 5/18) ≈ 8.18 seconds, demonstrating how direction critically changes the outcome.

How to Approach the Question

First, identify all the given data: length of the train (distance), speed of the train, and speed of the man.
Determine the direction of motion. The phrase 'same direction' is the key here.
Calculate the relative speed. For objects moving in the same direction, subtract the slower speed from the faster speed.
Check the units. The distance is in meters and speed is in km/hr. Convert the speed to m/s by multiplying by 5/18 to ensure all units are consistent.
Apply the formula Time = Distance / Speed. The 'distance' is the length of the train, and the 'speed' is the relative speed you just calculated.
Perform the final calculation to find the time in seconds and match it with the given options.

Concept Tested & Keywords

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Practise the full NORCET 3 - 2022 (Shift-2)

Attempt every question from this paper in a timed mock, then review the full solution for each one.