Question

River is flowing at $3\text{km/h}$ in the west direction, and you can swim at a maximum speed of $5\text{km/h}$. Given, the river is $12\text{km}$ wide. If you are crossing in shortest path, how long will you take to cross the river?

Answer 1

Given that I am crossing the river in the shortest path, so my resultant velocity will be perpendicular to river flow, as shown in the below diagram.


From triangle law and considering pythagorean triplets,

$\text{R}=4\text{km/hr}$

This vertical component $($here $\text{R})$ is my velocity component that I'll be using to cross $12\text{km}$ wide river. i.e.,

$v=4\text{km/hr};d=12\text{km}$

We know that, time taken to cross the river will be given by,

$t=\frac{d}{v}$

$\therefore t=\frac{12}{4}=3\text{hr}$

Hence, option $\left(\text{C}\right)$ is the correct answer.