Question

A train travels from a city $A$ to city $B$ with a constant speed of $10\text{m/s}$ and returns back to city $A$ in half of the time taken to travel from $A$ to $B$. Find its average speed during the entire journey.

• A. $40\text{m/s}$
• B. $30\text{m/s}$
• C. $15\text{m/s}$
• D. $\frac{40}{3}\text{m/s}$

Answer 1

The correct option is D $\frac{40}{3}\text{m/s}$

Let distance between the two cities $A$ and $B$ be $x\text{m}$.
Speed of train while going from $A$ to $B$$=10\text{m/s}$
Time taken by train to travel from $A$ to $B$
$t_1=\frac{x}{10}$
and time taken by train to travel from $B$ to $A$
$t_2=\frac{t_1}{2}=\frac{x}{20}$

$\text{Average speed =}\frac{\text{total distance}}{\text{total time}}$
$v_{\text{avg}}=\frac{x+x}{\frac{x}{10}+\frac{x}{20}}$
$\therefore v_{\text{avg}}=\frac{2x}{\frac{x}{10}+\frac{x}{20}}=\frac{40}{3}\text{m/s}$