Question

A student while going to school on a school bus, observes the average speed of the bus to be 20 km/h. On his return trip along the same way, average speed is 30 km/h. What is the average speed of the bus during the entire journey?

Answer 1

Step 1: Given

Average speed while going to school = $20km{h}^{-1}$

Average speed while returning = $30km{h}^{-1}$

Step 2: Formula used and Calculation

Let the bus covers d km distance for one-way trip and returns back along the same path.

Time taken by bus to move from A to is

$t_{AB}=\frac{d}{20}$

Time taken by bus to return from B to A

$t_{BA}=\frac{d}{30}$

Average speed,

$v_{avg}=\frac{totaldistance}{totaltimetaken}$

$\Rightarrow v_{avg}=\frac{d+d}{t_{AB}+t_{BA}}$

$\Rightarrow v_{avg}=\frac{2d}{\frac{d}{20}+\frac{d}{30}}$

$\Rightarrow v_{avg}=\frac{2}{\frac{1}{20}+\frac{1}{30}}$

$\Rightarrow v_{avg}=\frac{2\times 60}{3+2}$

$\Rightarrow v_{avg}=24km{h}^{-1}$