Question

if A rows 4 km upstream and 8 km downstream taking 2 hours each, what would be speed of stream
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Answer 1

Given:

A rows 4 km upstream and 8 km downstream for 2 hours each.

To find:

Speed of stream.

Calculation:

Let Velocity of boat in still water be u and Velocity of stream be v ;

So, for upstream travel:

$\sf{ \therefore \: \dfrac{4}{u - v} = 2}$

$\sf{ = > \: \dfrac{2}{u - v} = 1}$

$\sf{ = > \: u - v = 2 \: \: \: \: ......(1)}$

So, for downstream travel:

$\sf{ \therefore \: \dfrac{8}{u + v} = 2}$

$\sf{ = > \: \dfrac{4}{u + v} = 1}$

$\sf{ = > \: u + v = 4 \: \: \: \: ......(2)}$

Subtracting eq.(1) from eq.(2) :

$\sf{ = > (u + v) - (u - v) = 4 - 2}$

$\sf{ = > 2v = 2}$

$\sf{ = > v = 1 \: km {hr}^{ - 1} }$

So, Velocity of stream is 1 km/hr.