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A body covers one-third of the distance with a velocity $υ_{1}$ , the second one-third of the distance with a velocity $υ_{2}$ and the remaining distance with a velocity $υ_{3}$ . The average velocity is:

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$\frac{υ_{1} υ_{2} + υ_{2} υ_{3} + υ_{3} υ_{1}}{3}$

$\frac{υ_{1} + υ_{2} + υ_{3}}{3}$

$\frac{υ_{1} υ_{2} υ_{3}}{3}$

$\frac{3 υ_{1} υ_{2} υ_{3}}{υ_{1} υ_{2} + υ_{2} υ_{3} + υ_{3} υ_{1}}$

answer is B.

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Detailed Solution

$v = \frac{s_{1} + s_{2} + s_{3}}{t_{1} + t_{2} + t_{2}}$

$= \frac{s}{\frac{s}{3 υ_{1}} + \frac{s}{3 υ_{2}} + \frac{s}{3 υ_{3}}}$

$= \frac{3 υ_{1} υ_{2} υ_{3}}{υ_{1} υ_{2} + υ_{2} υ_{3} + υ_{3} υ_{1}}$

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