One third of a journey is covered at a speed of 59 km/h, the next one third of the journey is covered at a speed of 35 km/h and the remaining distance of the journey is covered at a speed of 10 km/h. Find the average speed (in km/h, rounded off to 1 decimal place) for the whole journey.

1. A

   19.5

2. B

   24.6

3. C

   20.6

4. D

   22.2

Appeared in: DSSSB 12 August 2024

Explanation

• The average speed is calculated by dividing the total distance by the total time taken.
• The journey is split into three equal distance segments, so the time spent in each segment will be different.
• The time for each segment is calculated as Distance/Speed. These times are then summed to get the total time.
• The total distance (D) is divided by the total time [D * (601/12390)], which simplifies to 12390/601.
• The result is approximately 20.615 km/h, which rounds to 20.6 km/h.

Why Other Options Were Wrong

• Option A: This value is a result of a calculation error, likely during the addition of fractions to find the total time or an error in the final division.
• Option B: This value is incorrect and likely stems from a significant miscalculation or using an incorrect formula, rather than the standard Average Speed = Total Distance / Total Time method.
• Option D: This incorrect value likely arises from a mistake in the final division step (i.e., incorrectly dividing 12390 by 601).

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 as background academic context rather than a clinical decision trigger.
• This question tests a fundamental concept in quantitative aptitude: the distinction between the arithmetic mean and the true average speed.
• A common mistake is to calculate the arithmetic average of the speeds: (59 + 35 + 10) / 3 = 34.7 km/h. This is incorrect because the time spent traveling at each speed is different.
• The vehicle spends more time traveling at the slower speeds, which pulls the average speed down significantly from the arithmetic mean.

How to Approach the Question

• First, identify that the question asks for 'average speed' and involves segments of 'equal distance' but different speeds.
• Recall the fundamental formula: Average Speed = Total Distance / Total Time. Recognize that simply averaging the speeds is a common trap and is incorrect.
• Let the total distance be a variable (e.g., 'D'). Calculate the distance of each segment (D/3).
• For each segment, calculate the time taken using the formula: Time = Distance / Speed.
• Sum the times for all segments to find the total time of the journey. This will involve adding fractions.
• Finally, divide the total distance ('D') by the total time expression. The distance variable 'D' should cancel out, leaving you with the final numerical answer.

Concept Tested & Keywords

• Concept Tested: Calculation of Average Speed
• Stem keywords: average speed, journey, km/h, one third
• Lead-in keywords: Find, average speed
• Negative lead-in flag: false

Question ID

QOV2xIu35hC7j8QOOKXoIa

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