Question 25

A person travels three equal distances at a speed of 'a' km/hr, 'b' km/hr and 'c' km/hr respectively. What is the average speed for the whole journey?

Solution

Let the three equal distances be denoted by D.

Total Distance covered $$=D+D+D=3D$$

Total time travelled $$=\dfrac{D}{a}+\dfrac{D}{b}+\dfrac{D}{c}=D\left(\dfrac{ab+bc+ca}{abc}\right)$$

Average speed = Total Distance Covered / Total Time travelled

$$=\dfrac{3D}{D\left(\frac{ab+bc+ca}{abc}\right)}$$

$$=\dfrac{3abc}{\left(ab+bc+ca\right)}$$

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