Discover the Answer to This Mind-Boggling Riddle About Average Speeds

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The average speed for a round trip where one leg is driven at 40 km/hr and the return at 60 km/hr is 48 km/hr, calculated using the harmonic mean rather than the arithmetic mean. The formula used is 2 divided by the sum of the reciprocals of the speeds, which avoids the common mistake of averaging the two speeds directly. This calculation highlights the importance of understanding the difference between harmonic and arithmetic means in speed-related problems. The discussion emphasizes that many people initially miscalculate by simply averaging the two speeds. Understanding these concepts is crucial for accurately determining average speeds in similar scenarios.
Tom McCurdy
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You drive a car at a speed of 40 km/hr to a place and then 60 km/hr back... what is the average speed of the car.

I feel really stupid for asking this but its really making me mad..
 
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hahaha as soon as i posted it it was so obvious...

Set distance equal to one

t1=1/40 t2=1/60

\frac{\Delta d}{\Delta t}=avg vel

\frac{2}{\frac{1}{40}+\frac{1}{60}}
 
Which produces 48 km/hr as answer
 
You are correct. Often people make the obvious mistake to take the arithmetic mean, being (40+60)/2 = 50 but in this case, you need the harmonic mean :smile:
 
\frac{2}{\frac{1}{40}+\frac{1}{60}}
harmonic mean could be calculated slightly easier:
\frac{v_1 v_2}{\frac{v_1 + v_2}{2}}
 
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