A boat moves along the flow of river between two fixed points A and B. it takes `t_(1)` time when going downstream and takes `t_(2)` time when going upstream between these two points. What time it will take in still water to cover the distance equal to AB.

Explanation

`t_(1)=(AB)/(v_(b)+v_(R)) . T_(2)=(AB)/(v_(b)-v_(R))` or `v_(b)+v_(R)=(AB)/(t_(1))`
and `v_(b)-v_(R)=(AB)/(t_(2))rArr 2v_(b)=(AB)/(t_(1)+(AB)/(t_(2)))=AB((t_(1)+t_(2))/(t_(1)t_(2)))`
or `((2t_(1)t_(2))/(t_(1)+t_(2)))=(AB)/(v_(b))`= time taken by the boat to cover AB