Question

One car moving on a straight road covers one-third of the distance with $20km.h{r}^{-1}$ and the rest with $60km.h{r}^{-1}$. The average speed is

• A. $40km.h{r}^{-1}$
• B. $80km.h{r}^{-1}$
• C. $46\left(\frac{2}{3}\right)\mathrm{km}.h{r}^{-1}$
• D. $36km.h{r}^{-1}$

Answer 1

The correct option is D

$36km.h{r}^{-1}$

Explanation of the correct option:

Finding average speed:

Let $x$ be the total distance and $t_1,t_2$ be the time taken to cover distances $\frac{x}{3},\frac{2x}{3}$

Time required to cover first one- third distance is

$$\begin{gathered} t_1=\frac{\left({\displaystyle \frac{x}{3}}\right)}{20} \\ =\frac{x}{60}hr \end{gathered}$$

Similarly, the time required to cover remaining distance is

$$\begin{gathered} t_2=\frac{\left({\displaystyle \frac{2x}{3}}\right)}{60} \\ =\frac{x}{90}hr \end{gathered}$$

Now, the total time is

$$\begin{gathered} \therefore t_1+t_2=\left(\frac{x}{60}\right)+\left(\frac{x}{90}\right) \\ =\frac{x}{30}\left(\frac{5}{6}\right) \\ =\frac{x}{36}hr \end{gathered}$$

Now, the average speed is the ratio of total distance and total time taken so,

$\begin{array}{rcl}v& =& \frac{x}{t_1+t_2}\\ & =& \frac{x}{\left({\displaystyle \frac{x}{36}}\right)}\\ & =& 36km/hr\end{array}$

Thus, the average speed is $36km.h{r}^{-1}$

Hence, option (D) is the correct answer.