Question

A car travels half the distance with a constant speed of $40kmph$ and the remaining half with a constant speed of $60kmph$. The average speed of the car in $kmph$ is:

• A. $40$
• B. $45$
• C. $48$
• D. $50$

Answer 1

The correct option is C $48$

Speed of the car in the first half, $v_1=40kmph$

Speed of the car in the second half, $v_2=40kmph$

Let the distance travelled by the car, $d=2x$

We know,

$speed\left(v\right)=\frac{distance\left(d\right)}{time\left(t\right)}$

$\Rightarrow t=\frac{d}{v}$

Time taken to travel the first half, $t_1=\frac{x}{40}hours$

Time taken to travel the remaining half, $t_2=\frac{x}{60}hours$

Total time taken, $t=t_1+t_2$

$t=\frac{x}{40}+\frac{x}{60}hours$

average speed, $v_{avg}=\frac{\text{total distance}}{\text{total time}}=\frac{2x}{\frac{x}{40}+\frac{x}{60}}$

$v_{avg}=\frac{2x\times 120}{3x+2x}$

$v_{avg}=\frac{240}{5}$

$v_{avg}=48kmph$