A bus travelling along a straight highway covers one-third of the total distance between two places with a velocity $20 k m h^{- 1}$ . The remaining part of the distance was covered with a velocity of $30 k m h^{- 1}$ for the first half of the remaining time and with velocity $50 k m h^{- 1}$ for the next half of the time. Find the average velocity of the bus for its whole journey.

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Solution

Average velocity of bus to covers $\frac{2}{3} r d$ of total distance
$= \frac{30 + 50}{2} = 40 m / s$
Now average speed of whole journey $= \frac{\frac{1}{3} x \times 20 + \frac{2}{3} x \times 40}{x} = \frac{100}{3} m / s$

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