Question

A car travels a distance of 2000 m. If the first half distance is covered at 40 km/hour and the second half at velocity v and if the average velocity is 48 km/hour, then the value of v is :

• A. 56 km/hour
• B. 60 km/hour
• C. 50 km/hour
• D. 48 km/hour

Answer 1

The correct option is B 60 km/hour

If the car travels the distance $AB$ in time $t_1$

then,

$t_1=\frac{1}{40}hr\{speed=\frac{distance}{time}\}$

If the car travels the distance $BC$ in time $t_2$

then,

$t_2=\frac{1}{4}hr$

Now, Average speed $=\frac{totaldistancetravelled}{totaltimetaken}$

$\Rightarrow 48=\frac{2}{t_1+t_2}$

$\Rightarrow 2=48(t_1+t_2)$

$\Rightarrow 2=48[\frac{1}{40}+\frac{1}{4}]$

$\Rightarrow \frac{1}{4}+\frac{1}{40}=\frac{1}{24}$

$\Rightarrow \frac{1}{4}=\frac{1}{24}-\frac{1}{40}=\frac{5-3}{120}=\frac{2}{120}=\frac{1}{60}$

$\Rightarrow 4=60{\tan }^{-1}$