A car covers AB distance with first one-third at velocity v1 m/s . . .

Question : A car covers AB distance with first one-third at velocity v₁ m/s second one-third at v₂ m/s and last one-third at v₃ m/s. If v₃=3v₁, v₂=2v₁ and v₁=11 m/s then the average velocity of the car is ____________ m/s.

Doubt by Navya 

Solution : 

Let the total distance = 3x

so, one third of the total distance will be = 3x/3 = x

We know, 

Speed = Distance/Time

Time = Distance/speed

Time taken to cover the first one third distance 

t₁ = Distance/speed

t₁ = x/v₁

similarly, time taken to cover second and third one-third distances

t₂=x/v₂

t₃=x/v₃

Average velocity 

= Total distance covered / Total time taken 

v₁=11 m/s (Given)

v₂=2v₁ (Given) 

So V₂= 2×11 = 22 m/s

Also

v₃=3v₁ (Given) 

So V₃=3×11 = 33 m/s

Now , substituting the values of v₁, v₂ and v₃ in above expression

v_av=3(1)(2)(3)

v_av=18 m/s