An ambulance travels from Hospital A to Hospital B at an average speed of 60 km/h and returns along the same route at an average speed of 40 km/h. What is the average speed of the ambulance for the entire round trip?

1. A

   50 km/h

2. B

   48 km/h

3. C

   45 km/h

4. D

   52 km/h

Appeared in: NORCET 7 Prelims -2024

Explanation

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• The average speed is defined as the total distance traveled divided by the total time taken.
• A common mistake is to take the arithmetic average of the speeds, which is incorrect because the time spent traveling at each speed is different.
• Let the distance be 'd'. The time for the first leg is d/60 and for the return leg is d/40.
• The total distance is 2d and the total time is (d/60 + d/40) = 5d/120.
• Average speed = Total Distance / Total Time = 2d / (5d/120) = (2d * 120) / 5d = 240/5 = 48 km/h.

Why Other Options Were Wrong

• Option A: This is the result of incorrectly calculating the arithmetic mean of the two speeds ( (60 + 40) / 2 = 50 ). This method is only valid if the travel time for both legs of the journey is identical, which is not the case here.
• Option C: This value has no mathematical basis derived from the problem's data. It is an incorrect option likely included to test the student's ability to perform the correct calculation.
• Option D: This value is also mathematically incorrect. It is higher than the simple average and does not reflect the correct physics of the problem.

Related Visual

• Visual 1: Diagram. A simple diagram showing a path from 'Hospital A' to 'Hospital B'. An arrow pointing right is labeled '60 km/h', and an arrow pointing left along the same path is labeled '40 km/h'. This helps visualize the two parts of the round trip.
• Visual 2: Flowchart. A flowchart outlining the steps for the correct calculation: 1. Identify the two different speeds for the same distance. 2. Recall the formula: Average Speed = Total Distance / Total Time. 3. Assume a convenient distance (e.g., 120 km). 4. Calculate time for each leg (Time = Distance/Speed). 5. Sum the total distance and total time. 6. Divide total distance by total time to get the final answer.

Clinical Relevance

• Nursing practice connection: Knowing Calculation of average speed for a journey with different speeds for each leg helps nurses interpret findings accurately and avoid errors in routine assessment, medication administration, and patient teaching.
• While this is a math problem, the context of an ambulance highlights the importance of accurate time and travel calculations in emergency medical services (EMS).
• EMS dispatchers and ambulance crews need to estimate travel times accurately for resource management, planning inter-facility transfers, and providing estimated times of arrival (ETAs) to receiving hospitals.
• Understanding that factors like traffic (which can cause different speeds for each leg of a journey) affect overall travel time is crucial for logistical planning in healthcare.

How to Approach the Question

• First, identify that this is a calculation-based question asking for 'average speed' over a round trip with two different speeds.
• Recognize the common trap: do not simply average the two speeds (60 and 40). This is incorrect because the time spent at each speed is different.
• Recall the fundamental formula: Average Speed = Total Distance ÷ Total Time.
• To make the calculation easy, assume a convenient one-way distance. The least common multiple of the speeds (60 and 40) is 120. Let the distance be 120 km.
• Calculate the time for each part of the journey using Time = Distance ÷ Speed.
• Sum the distances for the round trip (120 km + 120 km) and the times for the round trip to find the total distance and total time.

Concept Tested & Keywords

• Concept Tested: Calculation of average speed for a journey with different speeds for each leg.
• Stem keywords: ambulance, average speed, round trip, 60 km/h, 40 km/h
• Lead-in keywords: What is

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QzPgPHjqvhdkbjvYGwQGxH

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