Question

A swimmer's speed in the direction of the flow of river is $16\text{km/h}$. Against the direction of flow of river, the swimmer's speed is $8\text{km/h}$. Calculate the swimmer's speed in still water and speed of flow of the river respectively..

• A. $12\text{km/h},4\text{km/h}$
• B. $10\text{km/h},3\text{km/h}$
• C. $10\text{km/h},4\text{km/h}$
• D. $12\text{km/h},2\text{km/h}$

Answer 1

The correct option is A $12\text{km/h},4\text{km/h}$

Let the direction of flow of river as $+ve$.
swimmer's speed in still water means speed of swimmer w.r.t river flow,
$v_{s,r}=v_s-v_r...\left(i\right)$
given that
where $v_s=$ speed of swimmer w.r.t ground
$v_r=$ speed of river flow w.r.t ground
$\Rightarrow$When swimming in direction of river flow
$v_s=+16\text{km/h}$
$\therefore v_{s,r}=16-v_r...\left(ii\right)$
$\Rightarrow$When swimming in direction opposite of river flow
($\because$ direction of swimmer will be $-ve$)
$v_s=-8\text{km/h}$
$\therefore -v_{s,r}=-8-(+v_r)...\left(iii\right)$
Adding Eq $\left(ii\right)\&\left(iii\right)$,
$-2v_r=-8$
$\therefore v_r=4\text{km/h}$
Hence, from Eq $\left(i\right)$,
$v_{s,r}=16-4=12\text{km/h}$
$\therefore$ option $\left(a\right)$ is correct.