One-third of a journey is covered at a speed of 37 km/h, the next one-third of the journey is covered at a speed of 62 km/h and the remaining journey is covered at a speed of 47 km/h. The average speed (in km/h, rounded off to 1 decimal place) for the entire journey is:

1. A

   46.6

2. B

   45.2

3. C

   47

4. D

   44.2

Appeared in: DSSSB 13 August 2024

Explanation

• The problem requires calculating the average speed for a journey divided into three equal distance segments, each covered at a different speed.
• For journeys with equal distance segments, the average speed is the harmonic mean of the individual speeds, not the simple arithmetic mean.
• The formula for average speed is Total Distance divided by Total Time.
• Let each one-third of the journey be a distance 'd'. The total distance is 3d. The time taken for each segment is t1 = d/37, t2 = d/62, and t3 = d/47.
• The average speed is calculated as: 3d / (d/37 + d/62 + d/47), which simplifies to 3 / (1/37 + 1/62 + 1/47).
• Performing the calculation: 3 / (0.0270 + 0.0161 + 0.0213) ≈ 3 / 0.0644 ≈ 46.56 km/h, which rounds to 46.6 km/h.

Why Other Options Were Wrong

• Option B: This value is incorrect and likely results from a calculation error, either in summing the reciprocals of the speeds or in the final division.
• Option C: This is one of the speeds given for a segment of the journey, not the average for the entire trip. A common mistake is to guess or wrongly assume one of the given values is the average.
• Option D: This value is mathematically incorrect and stems from a significant arithmetic error during the calculation.

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 distance segments as background academic context rather than a clinical decision trigger.
• While this is a general aptitude question, the underlying principle of calculating rates is fundamental in many areas of nursing.
• Nurses frequently calculate rates for IV infusions (mL/hour), medication administration over time, and understanding physiological rates like glomerular filtration rate (GFR).
• Accurate rate calculation is critical for patient safety to ensure correct dosage and fluid administration.

How to Approach the Question

• Step 1: Identify the core question. The problem asks for the 'average speed' for a journey divided into equal 'one-third' distance segments.
• Step 2: Recognize the key condition: the distances are equal. This means you cannot simply average the speeds arithmetically.
• Step 3: Recall the fundamental formula for average speed: Average Speed = Total Distance / Total Time.
• Step 4: Set up the calculation. Let the distance of each segment be 'd'. The total distance is 3d. The time for each segment is distance/speed (d/37, d/62, d/47).
• Step 5: Formulate the equation: Average Speed = 3d / (d/37 + d/62 + d/47). Notice that 'd' cancels out.
• Step 6: Solve the simplified equation: 3 / (1/37 + 1/62 + 1/47). Calculate the value and round it to the required number of decimal places.

Concept Tested & Keywords

• Concept Tested: Calculating average speed for a journey with equal distance segments.
• Stem keywords: average speed, journey, one-third, speed
• Lead-in keywords: average speed

Question ID

Q9OxjZGF0ay8VnKiH0nX7n

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