A particle travels the first half of its total distance along a straight line with a speed

‘v’ kmph and the next half, with a speed of 60kmph. If the average speed for the journey is 40kmph, the value of ‘v’ is                           

Given that a particle starts at A and reaches B

Let AB = s

C is the midpoint of AB

It is said to travelled from AC with speed $={\text{v}}_{\text{1}}$ $=v$

And C to B with speed $={\text{v}}_2$

We know ${\text{V}}_{\text{Avg}}=\frac{{\text{2v}}_{\text{1}}{\text{v}}_{\text{2}}}{{\text{v}}_{\text{1}}+{\text{v}}_{\text{2}}}$

(when body travels equal distances with different velocities)

$40=\frac{2\text{v}\left(60\right)}{\text{v}+60}$

$\left(\text{v}+60\right)40=120\text{v}$

$\text{40v}+\text{2400}=\text{120v}$

$\text{2400=120v}-\text{40v}$

 $\text{2400}=\text{80v}$

$\text{v}=\frac{2400}{80}=30$

$\text{v}=30\text{kmph}$