#### Question

A motorcyclist drives from place A to B with a uniform speed of 30 km h^{-1} and returns from place B to A with a uniform speed of 20 km h^{-1}. Find his average speed.

#### Solution

We have to find the average velocity of the entire journey. For this, we have the following information :

Speed from A to B = (v_{1}) = 30 m/s

Let the distance from A to B be (d).

Also, let the time taken to travel from A to B be (t_{1}).

`"Time" = "Distance travelled"/"Speed"`

we have :

t_{1} = `d/30`

Speed from B to A (v_{2}) = 20 m/s

Let the time taken to travel from B to A be (t_{2}).

Thus, we have :

t_{2} = `d/20`

Total time of journey :

= t_{1} + t_{2}

= `d/30 + d/20`

= `d/12`

Total distance travelled is 2d.

Therefore,

`"Average speed" = "Total distance travelled"/"Time"`

On putting the values to obtain the average speed of the motorcyclist, we get :

= `"(2d)12"/d`

= 24 km/hr