A train goes from A to B at a speed of 12 km/h and returns from B to A by the same route at 24 km/h. The average speed (in km/h) of the train during the two-way journey is:

1. A

   13

2. B

   18

3. C

   16

4. D

   14

Appeared in: DSSSB 14 August 2024

Explanation

• For a round trip covering the same distance at two different speeds, the average speed is the harmonic mean of the speeds.
• The correct formula to use is: Average Speed = (2 × v1 × v2) / (v1 + v2).
• Substituting the given values: v1 = 12 km/h and v2 = 24 km/h.
• Calculation: (2 × 12 × 24) / (12 + 24) = 576 / 36.
• The final result is 16 km/h.

Why Other Options Were Wrong

• Option A: The value 13 is a result of an incorrect calculation and has no mathematical basis in the context of this problem.
• Option B: This is the arithmetic mean or simple average of the two speeds ((12 + 24) / 2 = 18). This is incorrect because the time spent traveling at each speed is different.
• Option D: The value 14 is a result of an incorrect calculation and does not correspond to the correct formula for average speed in this scenario.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of average speed for a round trip with varying speeds as background academic context rather than a clinical decision trigger.
• This question assesses basic mathematical and analytical skills, which are part of the general aptitude section in many nursing entrance examinations.
• Understanding rates and averages is a foundational skill applicable in various contexts, including calculating medication dosages or infusion rates, although this specific problem is a classic physics question.
• What if the train traveled for an equal amount of time at each speed, instead of an equal distance? In that case, the average speed would be the simple arithmetic mean: (12 + 24) / 2 = 18 km/h.

How to Approach the Question

• Identify the core question: It asks for the average speed over a two-way journey where the distance is the same each way, but the speeds are different.
• Recognize that this is not a simple average. The correct formula for average speed in this case is the harmonic mean: (2 × v1 × v2) / (v1 + v2).
• Identify the given speeds: v1 = 12 km/h and v2 = 24 km/h.
• Substitute the values into the formula: (2 × 12 × 24) / (12 + 24).
• Calculate the result: 576 / 36 = 16.
• Be cautious of the common trap of calculating the arithmetic mean (12 + 24) / 2 = 18, which is offered as a distractor.

Concept Tested & Keywords

• Concept Tested: Calculation of average speed for a round trip with varying speeds.
• Stem keywords: train, speed, average speed, 12 km/h, 24 km/h
• Lead-in keywords: average speed

Question ID

QirPq1hBfGBnjEDezj1ciC

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