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_(B) = (AB) /(t_(1)) " and " V_(b) - V_(R) = (AB)/(t_(2))`
` rArr 2V_(2) = (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 teken by the boat to cover AB