Question

A man can row a boat at $4\text{km/hr}$ in still water. If he is travelling in a river where the current is $2\text{km/hr}$, how long will it take him to row $6\text{km}$ upstream and then back to his starting point ?

• A. $0.5\text{hr}$
• B. $1\text{hr}$
• C. $2\text{hr}$
• D. $4\text{hr}$

Answer 1

The correct option is D $4\text{hr}$

Given:
Velocity of boat in still water, $v_b=4\text{km/hr}$

Velocity of river, $v_r=2\text{km/hr}$

Time take to row $6\text{km}$ upstream will be

$t_1=\frac{\text{Distance}}{v_b-v_r}=\frac{6}{(4-2)}=3\text{hr}$

And time take to row $6\text{km}$ downstream is

$t_2=\frac{\text{Distance}}{v_b+v_r}=\frac{6}{(4+2)}=1\text{hr}$

$\therefore$ Total time $t$ will be

$t=t_1+t_2=3+1=4\text{hr}$.

Hence, option $\left(d\right)$ is correct.

$$\begin{array}{c}\text{Why this question?}\\ \text{Velocity of boat w.r.t river,}\overrightarrow{V_{br}}=\overrightarrow{V_{bg}}-\overrightarrow{V_{rg}}\end{array}$$