An aeroplane flies around a square the sides of which measure 100 kms. each. The aeroplane cover

step 1 In this question, we have to calculate the average speed around the square. Since the distance t

An aeroplane flies around a square the sides of which...

An aeroplane flies around a square the sides of which measure $100 \mathrm{kms}$. each. The aeroplane covers at a speed of $100 \mathrm{kms}$. per hour the first side, at $200 \mathrm{kms}$ per hour the second side, at $300 \mathrm{Kms}$. per hour the third side, and at $400 \mathrm{kms}$ per hour the fourth side. Use the correct mean to find the average speed round the square.

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Key Concepts

Time-Distance Relationship

Understanding the relationship between time, distance, and speed is essential. For each segment, the time taken is computed by dividing the segment distance by its corresponding speed. Summing these times yields the total time, which is used along with the total distance to calculate the overall average speed.

Harmonic Mean

When segments of a journey are of equal distance but traveled at different speeds, the average speed is given by the harmonic mean of those speeds, rather than the arithmetic mean. The harmonic mean is calculated as the number of segments divided by the sum of the reciprocals of the individual speeds, which properly weights the time spent at each speed.

Average Speed Calculation

Average speed is determined by dividing the total distance traveled by the total time taken. In problems where a journey is broken into segments with varying speeds, it is critical to compute the time for each segment (distance divided by speed) and then sum these times to obtain the total duration of the journey.

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