A motorboat covers a given distance in 6 ~h moving downstream on a river. It covers the same distance in 10 ~h moving upstream. The time it takes to cover the same distance in still water is

Step-by-step solution

If v _ w be the velocity of water and v _ b be the velocity of motorboat in still water. The distance covered by motorboat in moving downstream in 6 ~h is x = ( v _ b + v _ w ) 6 ...(i) Same distance covered by motorboat in moving upstream in 10 ~h is x = ( v _ b - v _ w ) 10 ...(ii) From Eqs. (i) and (ii), we have gathered ( v _ b + v _ w ) 6= ( v _ b - v _ w ) 10 v _ w = v _ b 4 x = ( v _ b + v _ w ) 6=7.5 v _ b gathered Time taken by the motorboat to cover the same distance in still water is t= x v_ b = 7.5 v_ b