A swimmer's speed in the direction of flow of a river is `12kmh^(-1)`. Against the direction
of flow of the river the swimmer's speed is `6kmh^(-1)`. Calculate the swimmer's speed in still water and the velocity of the river flow.

Explanation

Let `v_(s)andv_(r)` represent the velocities of the swimmer and river respectively with respect to ground.
`v_(s)+v_(r)=12" "…..(1)`
and `v_(s)-v_(r)=6" "…..(2)`
Adding the both equations (1) and (2) `2v_(s)=12+6=18kmh^(-1)orv_(s)=9kmh^(-1)`. From equation (1),
`9+v_(r)=12orv_(r)=3kmh^(-1)`
When the river flow and swimmer move in the same direction, the net velocity of swimmer is 12 kmph.