Just the average?

Algebra Level 3

Peter walks a distance a a with speed v = 6 km/h v = 6\text{ km/h} . Then he walks back the same distance with v = 12 km/h v = 12\text{ km/h} . What was his average speed in km/h \text{km/h} ?


The answer is 8.

Malte Liesenhoff by Malte Liesenhoff , 21, Germany

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2 solutions

Romain Milon
Jul 14, 2016

Given that his velocity on the way back is two times superior, we know that the first part was two times longer to travel. Thus, we can determine the average by weighing the velocities: 6 × 2 + 12 × 1 2 + 1 = 8 \frac{6\times2+12\times1}{2+1}=8

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Alex G
Jul 14, 2016

The average velocity is given by the harmonic mean of the two velocities. Let H n H_n denote the harmonic mean:

H n = 2 1 6 + 1 12 \large H_n=\dfrac{2}{\dfrac{1}{6}+\dfrac{1}{12}}

After some simple arithmetic:

H n = 8 \large H_n= 8

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