Question

A car travels $30\mathrm{km}$ at a uniform speed of $40\mathrm{km}/\mathrm{hr}$ and the next $30\mathrm{km}$ at a uniform speed of $20\mathrm{km}/\mathrm{hr}$. Find its average speed.

Answer 1

Step 1: Given Data:

First $30\mathrm{km}$ covered by car with speed $=40km/h$

First $30\mathrm{km}$ covered by car with time, $\frac{30km}{40km/h}$

Next $30\mathrm{km}$ covered by car with speed $=20km/h$

Next, $30\mathrm{km}$ covered by car with time, $\frac{30km}{20km/h}$

Suppose the average speed of the car is $=vkm/h$

Step 2: Calculation:

As we know the average speed of the journey is the ratio of total distance to total time,

$$\begin{gathered} Averagespeed=\frac{TotalDis\tan ce}{Totaltime}=\frac{30km+30km}{{\displaystyle \frac{30km}{40km/h}}+{\displaystyle \frac{30km}{20km/h}}} \\ v=\frac{60}{{\displaystyle \frac{30+60}{40}}}\Rightarrow v=\frac{60\times 40}{{\displaystyle 90}} \\ v=\frac{2400}{90}=26.67km/h \end{gathered}$$

Hence, average speed of car is; $26.67km/h$