A person travels from X to Y at 50 km/h and returns along the same route at a…
2024
A person travels from X to Y at 50 km/h and returns along the same route at a speed 50% higher. What is the average speed for the entire round trip?
Answer: B. 60 km/h — ConceptAverage speed is total distance divided by total time; it is not generally the arithmetic mean of the speeds. When equal distances are covered at…
- A.
62.5 km/h
- B.
60 km/h
- C.
62 km/h
- D.
64 km/h
Attempted by 3 students.
Show answer & explanation
Correct answer: B
Concept
Average speed is total distance divided by total time; it is not generally the arithmetic mean of the speeds.
When equal distances are covered at speeds u and v, the average speed is the harmonic mean 2uv/(u + v).
Application
Let the one-way distance be d km. The return speed is 50 + 50% of 50 = 75 km/h.
The total distance is 2d km.
The total time is d/50 + d/75 = (3d + 2d)/150 = d/30 hours.
The average speed is 2d ÷ (d/30) = 60 km/h.
Cross-check
Using the harmonic-mean formula, 2 × 50 × 75/(50 + 75) = 7500/125 = 60 km/h, confirming the same result.
Therefore, the average speed for the complete round trip is 60 km/h.