One person travels three sides of an equilateral triangle at a speed of 12 km/hr, 24 km/hr and 8 km/hr. Find his average speed (in km/hr).
12
Let each side of the equilateral triangle be \(d\) km, so the total distance covered is \(3d\) km.
Time on each side: \(t_{1} = \dfrac{d}{12}\), \(t_{2} = \dfrac{d}{24}\), \(t_{3} = \dfrac{d}{8}\).
Total time \(= \dfrac{d}{12} + \dfrac{d}{24} + \dfrac{d}{8} = \dfrac{2d + d + 3d}{24} = \dfrac{6d}{24} = \dfrac{d}{4}\) hours.
Average speed \(= \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{3d}{d/4} = 3d \times \dfrac{4}{d} = 12\) km/hr.
Hence, the average speed is 12 km/hr.
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