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

t = \frac{2 t_{1} t_{2}}{t_{1} + t_{2}}

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t = \frac{t_{1} t_{2}}{t_{1} + t_{2}}

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t = \frac{2 t_{2}}{t_{1} + t_{2}}

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t = \frac{2 t_{1}}{t_{1} + t_{2}}

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Solution

The correct option is A $t = \frac{2 t_{1} t_{2}}{t_{1} + t_{2}}$

Let $V_{b}$ be the velocity of the boat in still water and $V_{R}$ be the flow speed in the river.

For downstream:
$V_{b} + V_{R} = V_{r e l}$
$\Rightarrow V_{b} + V_{R} = \frac{x}{t_{1}} . . . . . (1)$

For upstream:
$V_{b} - V_{R} = V_{r e l}$
$\Rightarrow V_{b} - V_{R} = \frac{x}{t_{2}} . . . . . . (2)$

Adding equations $(1)$ and $(2)$ , we get:
$2 V_{b} = \frac{x}{t_{1}} + \frac{x}{t_{2}}$
$2 V_{b} = x (\frac{t_{1} + t_{2}}{t_{1} . t_{2}})$
but, $\frac{x}{V_{b}} = t$
$\Rightarrow t = \frac{x}{V_{b}} = \frac{2 t_{1} t_{2}}{t_{1} + t_{2}}$

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A boat takes t1 time while going downstream between two fixed points A and B, and takes t2 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 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