A car completes a journey in 6 hours. It covers half the...

A car completes a journey in 6 hours. It covers half the distance at $50 \mathrm{~km} / \mathrm{hr}$ and the rest at $70 \mathrm{~km} / \mathrm{hr}$
The length of the joumey is
(a) $165 \mathrm{~km}$
(b) $175 \mathrm{~km}$
(c) $185 \mathrm{~km}$
(d) None of these

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Key Concepts

Harmonic Mean for Speeds over Equal Distances

When equal distances are covered at different speeds, the average speed over the whole journey is given by the harmonic mean rather than the arithmetic mean. This concept is important because it appropriately weights the contribution of each speed based on the distance traveled under each condition, ensuring accurate calculation of the overall performance.

Speed-Distance-Time Relationship

This fundamental concept relates speed, distance, and time using the equation distance = speed × time. It is essential for solving problems where any two of these quantities are known and the third is to be determined, providing the foundation for analysis in various motion scenarios.

Segmenting a Journey

In many real-world problems, journeys are divided into segments where the conditions, such as speed or distance, may vary. Understanding how to partition the journey into parts and calculate the time taken for each segment is crucial, as the overall journey time or distance is the sum of the times or distances of these individual segments.

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