Question

A car covers 30 km at a uniform speed of 30 km/h. What should be its speed for the next 90 km if the average speed of the entire journey is 60 km/h?

Answer 1

Step 1: Given data

Total distance covered by the car= $(30km+90km)=120km$

The uniform speed of the car for first $30km$ = $30km{h}^{-1}$

Average Speed($v_{avg}$) = $60km{h}^{-1}$

Step 2: Calculation of the average speed of the car:

We know,

Average Speed = $\frac{Totaldistance}{Totaltimetaken}$

The time taken by the car to cover the first $30km$ with the uniform speed of $30m{s}^{-1}$, is given by;

$time=\frac{distance}{speed}$ ,

$t_1=\frac{30km}{30km{h}^{-1}}$

$t_1=1hr$

Now, let the speed of the car for next $90km$ is $xkm{h}^{-1}$ , then,

$t_2=\frac{90km}{xkm{h}^{-1}}$

$t_2=\frac{90}{x}hr$

Now, the average speed of the car will be given by;

$60km{h}^{-1}=\frac{120km}{t_1+t_2}$

$60=\frac{120}{1hr+\frac{90}{x}hr}$

$60=\frac{120}{\frac{x+90}{x}}$

$60=\frac{120x}{x+90}$

$60(x+90)=120x$

$x+90=\frac{120x}{60}$

$x+90=2x$

$\Rightarrow 2x-x=90$

$\Rightarrow x=90km{h}^{-1}$

Hence,

The speed of the car for the next $90km$ is $90km{h}^{-1}$ .