Question

A motorcyclist drives from A to B with a uniform speed of $30km/h$ and returns back with a speed of $20km/h$. Find its average speed.

Answer 1

Step 1: Given

Let the distance travelled from A to B be x. So, the total distance travelled be $2x$.

Speed from A to B: $S_1=30km/h$

Speed from B to A: $S_2=20km/h$

Step 2: Formula Used

$AverageSpeed=\frac{TotalDis\tan ce}{TotalTime}$

Step 3: Solution

Calculate the total time by adding the time taken from A to B and B to A. The time taken in going from A to B is $\frac{x}{30}h$ and from B to A is $\frac{x}{20}h$.

$$\begin{gathered} T=T_1+T_2 \\ =\frac{x}{30}+\frac{x}{20} \\ =\frac{3x+2x}{60} \\ =\frac{x}{12} \end{gathered}$$

Now calculate the average speed.

$$\begin{gathered} AverageSpeed=\frac{TotalDis\tan ce}{TotalTime} \\ =\frac{2x}{{\displaystyle \frac{x}{12}}} \\ =24km/h \end{gathered}$$

Hence, the average speed is $24km/h$.