If a car covers 2/5th of the total distance with v1 speed and 3/5th distance with v2 then average speed is

The correct option is 5v1v2/(3v1+2v2).

To find the average speed of the car, we use the fundamental formula for average speed:
Average Speed = (Total Distance) / (Total Time)

Let the total distance of the journey be represented by $d$.

According to the problem description:
- The first part of the journey covers a distance of $d_1=\frac{2}{5}d$ at a speed of $v_1$.
- The second part of the journey covers a distance of $d_2=\frac{3}{5}d$ at a speed of $v_2$.

We can calculate the time taken for each part of the journey using the relation $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$:

For the first part:
$t_1=\frac{d_1}{v_1}=\frac{2d}{5v_1}$

For the second part:
$t_2=\frac{d_2}{v_2}=\frac{3d}{5v_2}$

Now, the total time $T$ is the sum of $t_1$ and $t_2$:
$T=t_1+t_2=\frac{2d}{5v_1}+\frac{3d}{5v_2}$

Taking a common denominator to add the terms:
$T=\frac{d}{5}(\frac{2}{v_1}+\frac{3}{v_2})=\frac{d}{5}\left(\frac{2v_2+3v_1}{v_1{v}_2}\right)$

Now, substitute the total distance $d$ and the total time $T$ into the average speed formula:
$v_{\text{avg}}=\frac{d}{T}=\frac{d}{\frac{d}{5}\left(\frac{3v_1+2v_2}{v_1{v}_2}\right)}$

Simplifying the expression by cancelling the common term $d$ from the numerator and denominator:
$v_{\text{avg}}=\frac{5}{\frac{3v_1+2v_2}{v_1{v}_2}}$