Question

A ferry boat transfers passengers between boat jetty $A$ and$B$, where $B$ is across the river downstream as shown. The boat goes from $A$ to $B$ and then comes back after waiting for $12min$. While going from $A$ to$B$, the boat moves with minimum velocity relative to water and while coming back it moves with double the minimum velocity relative to water as for going from $A$ to $B$. If river stream has a speed of $5km/h$ and distance between $A$ and $B$ is $1km$, then the total time (in minute) for the whole trip i.e., going from $A$ to $B$, waiting and then coming back to $A$, will be

Answer 1

For ${\overrightarrow{v}}_{BR}$ to be minimum,
$v_R\sin {60}^{\circ }=v_{BR}$
$v_{BR}=\frac{5\sqrt{3}}{2}km/h$
$t_1=\frac{AB\sin {60}^{\circ }}{V_{BR}\sin {30}^{\circ }}=\frac{2}{5}h=24min$
Waiting time, $t_2=12min$
When boat starts return, then $v_{BR}=2\times \left(\frac{5\sqrt{3}}{2}\right)km/h=5\sqrt{3}km/h$
$v_{BG}=5km/h$
$t_3\times v_{BG}=AB$
$t_3=\frac{1}{5}h=12min$
Total time, $t_1+t_2+t_3=24+12+12$
$=48min$