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.

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Solution

## Step 1. Given data:Motorcyclist speed from A to B = $30{\mathrm{kmh}}^{-1}$ Motorcyclist speed from B to A = $20{\mathrm{kmh}}^{-1}$Let the distance from A to B is D km.Distance for the entire journey is $2D$ km.Step 2. Formula used: Time taken $\left(T\right)$ = Distance$\left(D\right)$/ Speed $\left(v\right)$Step 3. Calculations: So, the total time taken $T$ is$T=\left(\frac{D}{30}\right)+\left(\frac{D}{20}\right)\phantom{\rule{0ex}{0ex}}=\frac{2D+3D}{60}=\frac{5D}{60}=\frac{D}{12}Hrs.$Average speed = Total distance/Total time.Average speed = $\frac{2D}{\frac{D}{12}}=\frac{2D×12}{D}=24{\mathrm{kmh}}^{-1}$Hence, the average speed of the motorcycle is $24{\mathrm{kmh}}^{-1}$.

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