Question

A swimmer can swim 10 km in 2 hours when swimming along the flow of a river. While swimming against the flow, she takes 5 hours for the same distance. Her speed in still water (in km/h) is

Answer 1

Let velocity of swimmer in still water = x Velocity of river flow = y
(i) Swimming along the river flow Resultant velocity of swimmer = x + y
$\Rightarrow 2=\frac{10}{x+y}$ $\Rightarrow x+y=5...\left(i\right)$
(ii) Swimming against the river flow Resultant velocity of woman = x - y $\Rightarrow 5=\frac{10}{x-y}$ $x-y=2...\left(ii\right)$
Adding equations (i) and (ii)
$2x=7$
$x=3.5km/h$