Question

A train travels with a speed of $60$ km/h from station A to station B and then comes back with a speed $80$ km/h from station B to station A. Find the average speed of train.

Answer 1

We know,
Average speed $=\frac{\text{total distance covered}}{\text{total time taken}}$
Let the distance between two stations be $d\text{km}$
So total distance travelled $=d+d=2d$
Total time taken $=$ travel time from station A to B+ travel time from station B to A
$=\frac{\left(\text{distance travelled from station A to B}\right)}{\text{speed}}+\frac{\text{(distance travelled from station B to A)}}{\text{speed}}$

$=\frac{d}{60}hrs+\frac{d}{80}hrs$

Average speed, $\left(v_{\text{avg}}\right)=\frac{(d+d)km}{\frac{d}{60}hrs+\frac{d}{80}hrs}$
$=\frac{2d}{\frac{4d+3d}{240}}\text{km}/\text{h}=\frac{2d}{7d}\times 240=\frac{480}{7}\text{km}/\text{h}$

Average speed $=68.57\text{km}/\text{h}$

Hence, average speed of train is $68.57\text{km}/\text{h}$.