Question

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

• A. $\frac{2v_1{v}_2}{v_1+v_2}$
• B. $\frac{5v_1{v}_2}{3v_1+2v_2}$
• C. $\frac{1}{2}\sqrt{v_1{v}_2}$
• D. $\frac{v_1+v_2}{2}$

Answer 1

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

Step 1, Given data

$2/5^{th}$ of the total distance with $v_1$ speed

$3/5^{th}$ distance with $v_2$ speed

Step 2, Finding the average speed

Let the total distance traveled by the car is $x$

So, as per the question, total time taken by the car to cover the whole distance is
$t=\frac{2x/5}{v_1}+\frac{3x/5}{v_2}$
Thus, average speed of the car is given by

$Averagespeed=\frac{Totaldistance}{Totaltime}$

Or,

$\frac{x}{t}=\frac{x}{\frac{2x/5}{v_1}+\frac{3x/5}{v_2}}=\frac{5v_1{v}_2}{3v_1+2v_2}$

Hence the average speed is $\frac{5v_1{v}_2}{3v_1+2v_2}$