One person travels on through the sides of an equilateral triangle at a speed of 12 kmph, 24 kmph, and 8 kmph. Find the average speed of it. (In kmph)

Given:

The speed of the man is 12 km/h, 24 km/h and 8 km/h

Concept Used:

Average speed = total distance/total time

The sides of an equilateral triangle are equal.

Calculation:

Let, the side of the triangle be x km.

As we know,

Time to cover x km distance at a speed of 12 km/hr = x/12 hrs

Time to cover x km distance at a speed of 24 km/hr = x/24 hrs

Time to cover x km distance at a speed of 8 km/hr = x/8 hrs

Total distance covered by the man = (x + x + x) = 3x

Total time to cover the distance (x/12 + x/24 + x/8)

∴ Average speed \( = \frac{{3x}}{{\frac{x}{{24}} + \frac{x}{{12}} + \frac{x}{8}}}\)

⇒ \(\frac{{3x}}{{\frac{{x + 2x + 3x}}{{24}}}}\)

⇒ 3x / (6x/24)

⇒ 1/2 × 24 = 12 kmph

∴ The average speed of the person is 12 km/h.