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

Solution

✅ Correct Option: 4
  1. For equal distances at different speeds:

Average speed = Total DistanceTotal Time\frac{\text{Total Distance}}{\text{Total Time}}

  1. If each section is dd distance:

Total distance = 3d3d

Total time = da+db+dc\frac{d}{a} + \frac{d}{b} + \frac{d}{c}

  1. Average Speed = 3dda+db+dc\frac{3d}{\frac{d}{a} + \frac{d}{b} + \frac{d}{c}}

= 3dd(bc+ac+ab)abc\frac{3d}{\frac{d(bc + ac + ab)}{abc}}

= 3abc(ab+bc+ac)\frac{3abc}{(ab + bc + ac)}

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