A person travels along the sides of an equilateral triangular field at speeds of 36 km/h, 30 km/h and 45 km/h. Find his average speed.
36 km/h
The three sides of an equilateral triangle are equal, so the person covers equal distances at the three speeds.
For equal distances, average speed = \(\frac{3}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}}\).
Here \(\frac{1}{36}+\frac{1}{30}+\frac{1}{45} = \frac{5+6+4}{180} = \frac{15}{180} = \frac{1}{12}\).
So the average speed works out to \(3 \times 12 = 36\) km/h, the harmonic mean of the three speeds.
Hence, 36 km/h.
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