Question

A boat takes $t_1$ time while going downstream between two fixed points $A$ and $B$, and takes $t_2$ time while going upstream through the same distance. If river does not flow, then the time taken by the boat to cover the same distance is

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

Answer 1

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


Let $V_b$ be the velocity of the boat in still water and $V_R$ be the flow speed in the river.

For downstream:
$V_b+V_R=V_{rel}$
$\Rightarrow V_b+V_R=\frac{x}{t_1}.....\left(1\right)$

For upstream:
$V_b-V_R=V_{rel}$
$\Rightarrow V_b-V_R=\frac{x}{t_2}......\left(2\right)$

Adding equations $\left(1\right)$ and $\left(2\right)$, we get:
$2V_b=\frac{x}{t_1}+\frac{x}{t_2}$
$2V_b=x\left(\frac{t_1+t_2}{t_1.t_2}\right)$
but, $\frac{x}{V_b}=t$
$\Rightarrow t=\frac{x}{V_b}=\frac{2t_1{t}_2}{t_1+t_2}$