Question

If a car covers $\frac{2}{5}th$ of the total distance with $v_1$ speed and $\frac{3}{5}th$ of the total distance with $v_2$ speed, then the average speed of the car is

• A. $\frac{v_1{v}_2}{2v_1+3v_2}$
• B. $\frac{v_1+v_2}{2}$
• C. $\frac{{5v}_1{v}_2}{2v_1+3v_2}$
• D. $\frac{{5v}_1{v}_2}{3v_1+2v_2}$

Answer 1

The correct option is D $\frac{{5v}_1{v}_2}{3v_1+2v_2}$

It is given that v1 and v2 are the speeds of the car required to cover $\frac{2}{5}th$ and $\frac{3}{5}th$ of the total distance, respectively.
Let s be the total distance travelled by the car.
Time taken by the car to cover $\frac{2}{5}th$ of total distance, $t_1=\frac{\frac{2}{5}s}{v_1}$
Time taken by the car to cover $\frac{3}{5}th$ of total distance, $t_2=\frac{\frac{3}{5}s}{v_2}$
$\text{Average speed}=\frac{\text{Total distance travelled}}{\text{Total time taken}}$
$v_{av}=\frac{s}{t_1+t_2}$
$v_{av}=\frac{s}{\frac{2}{5}\times \frac{s}{v_1}+\frac{3}{5}\times \frac{s}{v_2}}$
$v_{av}=\frac{s}{\frac{s}{5}(\frac{2}{v_1}+\frac{3}{v_2})}$
$v_{av}=\frac{{5v}_1{v}_2}{3v_1+2v_2}$
Hence, the correct answer is option (d).