Question 16
A motorcyclist drives from A to B with a uniform speed of $30 k m p h$ and returns back with a speed of $20 k m p h$ . Find its average speed.

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Solution

Let distance covered, AB = x.
Therefore total distance traveled = 2x.
Let $t_{1}$ be the time taken to move from A to B and speed $v_{1} = 30 k m p h$ .
$t_{2}$ be the time taken to move from B to A and speed $v_{2} = 20 k m p h$ .
We know $t i m e = \frac{d i s t a n c e}{s p e e d}$
$t_{1} = \frac{x}{30}$ and $t_{2} = \frac{x}{20}$
Total time $= t_{1} + t_{2} = \frac{5 x}{60}$ .
Average speed for entire journey
$= \frac{T o t a l d i s t a n c e}{T o t a l t i m e} = \frac{2 x}{\frac{5 x}{60}} = 24 k m p h$

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