An aeroplane flies along the sides of an equilateral triangle with speed of…

Step-by-Step Solution

When an object travels equal distances at different speeds, the average speed is calculated using the harmonic mean.

Identify the variables:

• The aeroplane travels along the three sides of an equilateral triangle, meaning the distance for each segment is equal.

• Speeds: x = 300 km/hr, y = 200 km/hr, z = 240 km/hr.

• Apply the average speed formula for three equal distances:

  • Average Speed = (3 * x * y * z) / (xy + yz + zx)

• Perform the calculation:

  • Numerator = 3 * 300 * 200 * 240 = 43,200,000

  • Denominator = (300 * 200) + (200 * 240) + (300 * 240)

  • Denominator = 60,000 + 48,000 + 72,000 = 180,000

  • Average Speed = 43,200,000 / 180,000 = 240 km/hr.