A train travels 1/3 of the total distance at 40km/hr, 1/4 of the total distance at 60km/hrand the remaining distance at 50km/hr. Find the average speed of the train.

1. A

   50 km/hr

2. B

   42 km/hr

3. C

   45 km/hr

4. D

   48 km/hr

Appeared in: RRB Nsg. Superintendent-2026 (Shift -2nd)

Explanation

• PThe fundamental formula for average speed is Total Distance divided by Total Time.
• The journey is broken into three segments. The time for each segment is calculated using the formula Time = Distance / Speed.
• The first segment (D/3 at 40 km/hr) takes D/120 hours.
• The second segment (D/4 at 60 km/hr) takes D/240 hours.
• The remaining segment (5D/12 at 50 km/hr) takes D/120 hours.
• The total time is the sum of these individual times: (D/120 + D/240 + D/120) = D/48 hours.

Why Other Options Were Wrong

• Option A: 50 km/hr is the speed of the final segment of the journey, not the average for the entire trip. It is also the simple arithmetic mean of the three speeds (40 + 60 + 50) / 3 = 50, which is an incorrect method for calculating average speed when distances are different.
• Option B: 42 km/hr is the result of a calculation error. It does not correspond to the correct application of the average speed formula.
• Option C: 45 km/hr is the result of a calculation error. It does not correspond to the correct application of the average speed formula.

Related Visual

• Visual 1: Flowchart: A flowchart illustrating the step-by-step process: 1. Assume total distance 'D'. 2. Calculate Time = Distance/Speed for each of the three segments. 3. Sum the times to get Total Time. 4. Calculate Average Speed = D / Total Time.

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 over different fractional distances as background academic context rather than a clinical decision trigger.
• This question tests foundational numeracy and problem-solving skills, which are essential for various calculations in healthcare.
• Nurses frequently use calculations for medication dosages, IV drip rates, and fluid balance, all of which require a strong grasp of mathematical principles like rates and proportions.
• What if the train traveled for equal amounts of time at each speed instead of equal distances? In that case, the average speed would be the simple arithmetic mean: (40 + 60 + 50) / 3 = 50 km/hr.

How to Approach the Question

• First, identify the core task: calculating the average speed of a journey with multiple parts.
• Recall the fundamental formula: Average Speed = Total Distance / Total Time.
• Recognize that you cannot simply average the speeds. You must calculate the total time taken.
• To make calculations easier, assume a variable for the total distance, such as 'D' or a convenient number like the LCM of the denominators (3 and 4) and speeds, e.g., 600 km.
• Calculate the time taken for each segment of the journey using the formula: Time = Distance / Speed.
• Sum the times for all segments to find the total time of the journey.

Concept Tested & Keywords

• Concept Tested: Calculation of average speed for a journey with variable speeds over different fractional distances.
• Stem keywords: train, travels, total distance, km/hr, average speed
• Lead-in keywords: Find

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