Multiple choice

An aeroplane travels a distance in the form of a square with the speeds of 400 km/hr. 600 km/hr, 800 km/hr and 1,200 km/hr respectively. Find the average speed for the whole distance along the four sides of the square.

  1. 640 km/hr

  2. 620 km/hr

  3. 630 km/hr

  4. 650 km/hr
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A Correct answer
Explanation

Average speed for a square path with sides of length L is total distance (4L) divided by total time. Time = L/400 + L/600 + L/800 + L/1200. Common denominator is 2400. Time = L(6+4+3+2)/2400 = 15L/2400 = L/160. Average speed = 4L / (L/160) = 4 * 160 = 640 km/hr.

AI explanation

Since the aeroplane travels along the four equal sides of a square at different speeds, we use the harmonic mean formula for four speeds. The average speed is calculated as 4 divided by the sum of the reciprocals of the speeds. Evaluating 4 divided by (1/400 + 1/600 + 1/800 + 1/1200) gives 640 km/hr.

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