A person covers 1/4 of the distance at a speed of 15 km/h and 1/3 of the distance at a speed of 30 km/h. The remaining distance is covered by the same person at a speed of 45 km/h. What is the average speed for the entire journey?

1. A

   27

2. B

   20

3. C

   37

4. D

   30

Appeared in: Haryana CHO - 2022

Explanation

• The average speed is calculated by dividing the total distance traveled by the total time taken.
• The journey is broken into three segments with different speeds and distances.
• First, calculate the distance of each segment. The remaining distance is the total minus the sum of the first two parts: 1 - (1/4 + 1/3) = 1 - 7/12 = 5/12 of the total distance.
• Next, calculate the time taken for each segment using the formula: Time = Distance / Speed.
• Sum the times for all three segments to get the total time.
• Finally, divide the total distance by the total time to find the average speed, which results in 27 km/h.

Why Other Options Were Wrong

• Option B: The value 20 represents the total time taken for the journey (in hours) based on the assumed distance of 540 km, not the average speed.
• Option C: The value 37 does not result from any standard calculation related to average speed. It is likely an arbitrary number included as a distractor.
• Option D: This is the simple arithmetic mean of the three speeds: (15 + 30 + 45) / 3 = 30 km/h. This is incorrect because the person did not spend an equal amount of time traveling at each speed.

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 journey with variable speeds and distances as background academic context rather than a clinical decision trigger.
• This question tests basic numeracy and problem-solving skills, which are essential for various calculations in professional settings, including dosage calculations, fluid balance monitoring, and data interpretation in healthcare.
• What if? If the person spent an equal amount of time in each segment instead of covering fractional distances, the average speed would be the simple arithmetic mean of the speeds: (15 + 30 + 45) / 3 = 30 km/h.

How to Approach the Question

• First, identify that the question asks for the average speed, not the average of the speeds.
• Recall the correct formula: Average Speed = Total Distance / Total Time.
• To make calculations easier, assume a convenient total distance. A good choice is a number that is a multiple of the denominators of the given fractions (4 and 3), such as 12, 120, or 540.
• Calculate the distance for each part of the journey based on the assumed total distance.
• Calculate the time taken for each part using the formula Time = Distance / Speed.
• Sum the individual times to find the total time for the entire journey.

Concept Tested & Keywords

• Concept Tested: Calculation of average speed for a journey with variable speeds and distances.
• Stem keywords: average speed, distance, speed, 1/4 of the distance, 1/3 of the distance, remaining distance
• Lead-in keywords: What is

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Q32vzJnb5PryT2gDHOgD6f

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