Question

A boat takes two hours to travel $8\text{km}$ and back in still water. If the velocity of water is $4\text{km/h}$, the time taken for going upstream $8\text{km}$ and coming back is

• A. Cannot be estimated with the information given
• B. $2h$
• C. $1h20min$
• D. $2h40min$

Answer 1

The correct option is D $2\text{h}40\text{min}$

Given:
Boat covers distance of $16\text{km}$ in a still water in $2\text{hours}$.
i.e., velocity of boat
$\left(v_B\right)=\frac{16}{2}=8\text{km/h}$
Now velocity of water
$v_w=4\text{km/h}$

Time taken for going upstream
$t_1=\frac{\text{distance}}{v_{Bw}}{t}_1=\frac{8\text{km}}{v_B-v_w}=\frac{8\text{km}}{8\text{km/h}-4\text{km/h}}{t}_1=2\text{h}$

As we know water current oppose the motion of boat
Therefore,
Time taken for going down stream
$t_1=\frac{\text{distance}}{v_{Bw}}{t}_1=\frac{\text{distance}}{v_B-(-v_w)}{t}_2=\frac{8\text{km}}{v_B+v_w}=\frac{8\text{km}}{8\text{km/h}+4\text{km/h}}{t}_2=\frac{8}{12}\text{h}T=t_1+t_2$
(As water current helps the motion of boat)
Hence,
Total time $T=t_1+t_2=(2+\frac{8}{12})hrT=2\text{h}40\text{min}$