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Hariteja walked to his school at a speed of 4┬аkm/h and returned on a scooter at 20┬аkm/h. His average speed during the two-way journey is:
12┬аkm/h
6┬аkm/h
320тАЛ┬аkm/h
8┬аkm/h
320тАЛ┬аkm/h
Use the Harmonic Mean formula for two equal distances: (2v1v2)/(v1+v2). For 4 and 20: (2420)/(4+20) = 160/24 = 20/3 km/h.
Walking speed to school (v1) = 4 km/h, Return speed on scooter (v2) = 20 km/h
Average┬аSpeed=v1тАЛ+v2тАЛ2├Чv1тАЛ├Чv2тАЛтАЛ
Use the Harmonic Mean formula for two equal distances: (2v1v2)/(v1+v2). For 4 and 20: (2420)/(4+20) = 160/24 = 20/3 km/h.
A common mistake is taking the simple arithmetic mean, (4+20)/2 = 12 km/h, which is incorrect because the time taken for each leg of the journey is different.
Identify given variables
Speed while going (v1тАЛ) = 4 km/h. Speed while returning (v2тАЛ) = 20 km/h.
v1тАЛ=4,v2тАЛ=20
Apply average speed formula
Since the distance covered in both directions is the same, we use the harmonic mean formula: Average┬аSpeed=v1тАЛ+v2тАЛ2v1тАЛv2тАЛтАЛ
Avg=4+202├Ч4├Ч20тАЛ
Calculate the result
Substitute the values: Avg=24160тАЛ. Simplifying by dividing both numerator and denominator by 8, we get Avg=320тАЛ km/h.
Avg=320тАЛ┬аkm/h
C is correct because the average speed calculated using the harmonic mean formula is 20/3 km/h.
This formula is a standard shortcut for any problem involving two constant speeds over equal distances, often seen in work-efficiency problems (Time and Work) as well.
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