Question

A boat covers certain distance between two spots on a river taking ${}^{\prime }{t}_1^{\prime }$ time, going down stream and ${}^{\prime }{t}_2^{\prime }$ time going upstream, what time will be taken by the boat to cover the same distance in still water :-

• A. $\frac{t_1+t_2}{2}$
• B. $\frac{t_1}{2}$ + $\frac{3}{4}$$t_2$
• C. $\frac{2t_1{t}_2}{t_1+t_2}$
• D. $\frac{t_1+t_2}{2t_1{t}_2}$

Answer 1

The correct option is C $\frac{2t_1{t}_2}{t_1+t_2}$

Let the velocity of a boat in still water is u and velocity of the river is v and distance is d

down the stream speed will add total velocity is u+v it takes time t_{1}

in upstream speed will be subtracted total velocity is u-v it take time t_{2}

$u+v=\frac{d}{t_1}$ eq(1)..

$u-v=\frac{d}{t_2}$ eq(2)..

$2U=\frac{d}{t_1}+\frac{d}{t_2}$

$u=\frac{d(t_1+t_2)}{2t_1{t}_2}$

time take by the still boat is $t=\frac{d}{u}=\frac{2t_1{t}_2}{(t_1+t_2)}$

Hence C option is correct