One-third of a journey is covered at a speed of 21 km/h, the next one-third of the journey is covered at a speed of 63 km/h and the remaining journey is covered at a speed of 86 km/h. The average speed (in km/h, rounded off to 1 decimal place) for the entire journey is:

1. A

   41.6

2. B

   38.6

3. C

   39.9

4. D

   43.4

Appeared in: DSSSB 14 August 2024

Explanation

• The question involves calculating the average speed for a journey divided into three equal distance segments, each with a different speed.
• For equal distances, the correct method is to calculate the harmonic mean of the speeds, not the simple arithmetic average.
• The formula for the harmonic mean of three speeds (v₁, v₂, v₃) is: Average Speed = 3 / (1/v₁ + 1/v₂ + 1/v₃).
• Applying this formula: 3 / (1/21 + 1/63 + 1/86) gives approximately 39.9 km/h.
• The calculation (3 × 21 × 63 × 86) / ((21 × 63) + (63 × 86) + (86 × 21)) results in 341334 / 8547, which is approximately 39.9 km/h.

Why Other Options Were Wrong

• Option A: This is an incorrect calculation. It does not correspond to the harmonic mean or any other standard method for calculating average speed in this context.
• Option B: This value is also a result of an incorrect calculation and is lower than the correctly calculated harmonic mean.
• Option D: This is an incorrect calculation. A common mistake is to calculate the arithmetic mean (simple average) of the speeds, which would be (21 + 63 + 86) / 3 = 56.7 km/h. This option is not the arithmetic mean, but it is also an incorrect result.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating average speed for a journey with equal distances covered at different speeds as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude, a component of many nursing entrance exams designed to assess problem-solving and mathematical reasoning skills.
• While not a direct clinical skill, the logical thinking required to solve such problems is essential for nurses in tasks like medication dosage calculation, interpreting lab trends, and managing infusion rates.
• What if the journey was divided into three equal time intervals instead of distances? In that case, the average speed would be the simple arithmetic mean: (21 + 63 + 86) / 3 = 56.7 km/h.

How to Approach the Question

• First, identify the key information: the journey is divided into three equal distances ('one-third each').
• Recognize that the speeds for these equal distances are different (21, 63, and 86 km/h).
• Recall the rule: To find the average speed for equal distances covered at different speeds, you must use the harmonic mean, not the simple arithmetic mean.
• Apply the formula for the harmonic mean of three speeds: Average Speed = 3 / (1/v₁ + 1/v₂ + 1/v₃), or the equivalent form: (3 × v₁v₂v₃) / (v₁v₂ + v₂v₃ + v₃v₁).
• Substitute the given speeds into the formula and perform the calculation carefully.
• Round the final answer to one decimal place as requested by the question and match it with the given options.

Concept Tested & Keywords

• Concept Tested: Calculating average speed for a journey with equal distances covered at different speeds.
• Stem keywords: average speed, one-third of a journey, 21 km/h, 63 km/h, 86 km/h
• Lead-in keywords: The average speed
• Negative lead-in flag: false

Question ID

Qi1sbZI9YqaWGYegawSnjH

Copy ID

Reference Book

E6 NursingResearch Sukhpal Kaur p. 441-443