Question

An athlete runs in a straight line from point $X$ to point $Y$ at a constant speed of $3m/s$, and then return back along the same path from $Y$ to $X$ at a constant speed of $6m/s$ . Find out her average speed for the entire run?

• A. $3.5m/s$
• B. $4m/s$
• C. $4.5m/s$
• D. $5m/s$
• E. $5.5m/s$

Answer 1

The correct option is B $4m/s$

Let the distance between points $X$ and $Y$ be $d$.

Journey from X to Y : Speed $v_1=3m/s$

Time taken $t_1=\frac{d}{3}$ ........(1)

Journey from Y to X : Speed $v_2=6m/s$

Time taken $t_2=\frac{d}{6}$ ........(2)

Thus total time taken by athlete to run $2d$ distance $t=\frac{d}{3}+\frac{d}{6}$

$\therefore$ Average speed $=\frac{2d}{\frac{d}{3}+\frac{d}{6}}=\frac{2\times 3\times 6}{3+6}=4m/s$