A man completes 30 km of a journey at 6 km/hour and the remaining 40 km of the journey at 5 hours. His average speed for the whole journey is

Appeared in: RRB Staff Nurse Mumbai-2015

Explanation

The formula for average speed is Total Distance divided by Total Time.
First, calculate the time for the first part of the journey: Time = Distance / Speed = 30 km / 6 km/hr = 5 hours.
The time for the second part of the journey is given as 5 hours.
Next, calculate the total distance and total time for the entire journey. Total Distance = 30 km + 40 km = 70 km. Total Time = 5 hours + 5 hours = 10 hours.
Finally, calculate the average speed: Average Speed = 70 km / 10 hours = 7 km/hr.

Option A: This answer (6 4/11 km/hr or 70/11 km/hr) is the result of a common mistake: dividing the total distance (70 km) by the sum of the first speed and the second time (6 km/hr + 5 hours = 11). This incorrectly mixes units of speed and time in the denominator.
Option C: This value (7.5 km/hr) might be obtained by incorrectly averaging the speeds of the two parts. The speed of the second part is 40 km / 5 hours = 8 km/hr. Averaging the two speeds (6 km/hr + 8 km/hr) / 2 gives 7 km/hr, not 7.5. This answer likely stems from a calculation error.
Option D: This is the speed of only the second part of the journey (40 km / 5 hours = 8 km/hr). The question asks for the average speed of the whole journey, not just a segment of it.

Visual 1: Diagram - A line representing the total journey, segmented into 'Part 1' (30 km, 5 hrs) and 'Part 2' (40 km, 5 hrs), visually demonstrating the components that sum to the total distance and 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 as background academic context rather than a clinical decision trigger.
While not a clinical question, this type of problem tests basic numeracy and analytical skills, which are essential for nurses.
Nurses frequently perform calculations for medication dosages, IV drip rates, and fluid balance, all of which require a strong foundation in mathematical reasoning.
What if the second part of the journey was 40 km at 8 km/hr? The time for the second part would still be 40/8 = 5 hours, and the final answer would remain the same, demonstrating that different inputs can lead to the same result.

How to Approach the Question

First, identify the core question: you need to find the 'average speed' for the 'whole journey'.
Recall the fundamental formula: Average Speed = Total Distance / Total Time.
Break the problem into its constituent parts. Here, there are two parts to the journey.
For each part, determine the distance traveled and the time taken. If one is missing, calculate it using the formula Speed = Distance / Time.
Sum the distances from all parts to find the Total Distance. Sum the times from all parts to find the Total Time.
Divide the Total Distance by the Total Time to get the final answer. Avoid the common trap of simply averaging the speeds of the different parts.

Concept Tested & Keywords

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