Question

A train travels from one station to another at a speed of 40 km/h and returns to the first station at a speed of 60 km/h. The average speed of the train is

• A. 48 km/h
• B. 40 km/h
• C. 50 km/h
• D. 60 km/h

Answer 1

The correct option is A 48 km/h

Let the first station be A and the second station be B.

Velocity of train from A to B, $v_1=40km/h$
Velocity of train from B to A, $v_2=60km/h$
Let s be the distance between the two stations A and B.
Time taken by the train to go from A to B, $t_1=\frac{s}{v_1}$
$\Rightarrow t_1=\frac{s}{40}$
Time taken by the train to go from B to A, $t_2=\frac{s}{v_2}$
$\Rightarrow t_2=\frac{s}{60}$
$\text{Average speed}=\frac{\text{Total distance travelled}}{\text{Total time taken}}$
Average speed, $v_{av}=\frac{s+s}{t_1+t_2}$
$\Rightarrow v_{av}=\frac{2s}{s(\frac{1}{v_1}+\frac{1}{v_2})}$
$\Rightarrow v_{av}=\frac{s+s}{\frac{s}{v_1}+\frac{s}{v_2}}$
$\Rightarrow v_{av}=\frac{2v_1{v}_2}{v_1+v_2}$
$\Rightarrow v_{av}=\frac{2\times 40\times 60}{40+60}=\frac{4800}{100}=48km/h$
Hence, the correct answer is option (a).