Question

A swimmer crosses a river with minimum possible time of $10 \,s$ and when he reaches the other end, he starts swimming in the direction towards the point from where he started swimming. Keeping the direction fixed, the swimmer crosses the river in $15 \,s$. The ratio of speed of swimmer with respect to water to the speed of river flow is $\sqrt{\frac{x}{y}}$. Find $(x+y)$.
(Assume constant speed of river and swimmer)

Answer 1

$15=\frac{10 V_{S R}}{V_{S R} \cos \theta}=\frac{10 V_{S R}}{V_{S R}\left(\frac{10 V_{S R}}{10 \sqrt{V_{R}^{2}+V_{S R}^{2}}}\right)}$
$\Rightarrow 15=10 \sqrt{\left(\frac{V_{R}}{V_{S R}}\right)^{2}+(1)}$
$\Rightarrow \frac{V_{S R}}{V_{R}}=\frac{2}{\sqrt{5}}$