Swati can row her boat at a speed of $5 k m / h$ in still water. It takes her $1$ hour more to row the boat $5.25 k m$ upstream than to return downstream. Find the speed of the stream.

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Solution

$L e t t h e s p e e d o f t h e s t r e a m b e x . T h e t o t a l d i s t a n c e t r a v e l l e d i s f i x e d (s a y x) .$

$S p e e d w h e n g o i n g u p s t r e a m = 5 + x$

$S p e e d w h e n g o i n g d o w n s t r e a m = 5 - x$

$D i s t a n c e = S p e e d * T i m e$

So,
$\frac{5.25}{5 + x} + 1 = \frac{5.25}{5 - x}$

$5.25 (5 + x - 5 + x) = (25 - x^{2})$

$10.5 x = 25 - x^{2}$

$x^{2} + 10.5 x - 25 = 0$

$(x - 2) (x + 12.5) = 0$

$x = 2$ km\hr is the speed of the stream

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