Question

A motar boat whose speed is 18km/hr in still water takes 1hr more to go 24 km upstream then to return downstream to the same spot.find the speed of the stream

Answer 1

Answer:

Let the speed of stream be x km / hr

For upstream = ( 18 - x ) km / hr

For downstream = ( 18 + x ) km / hr

A.T.Q.

24 / 18 - x - 24 / 18 + x = 1

48 x = 324 - x²

x² + 48 x - 324 = 0

( x + 54 ) ( x - 6 ) = 0

x = - 54 or x = 6

Since speed can't be negative .

Therefore , speed of the stream is 6 km / hr .

Answer 2

Given: Speed of Motorboat is 18km/hr.

❏ Let the speed of the stream be x km/hr.

Therefore,

Speed of Motorboat in downstream = (18 + x) km/hr.

And,

Speed of Motorboat in upstream = (18 - x) km/hr.

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$\underline{\boldsymbol{According\: to \:the\: Question :}}$ ⠀

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$:\implies\sf \dfrac{24}{18 - x} - \dfrac{24}{18+x} = 1 \\\\\\:\implies\sf \dfrac{24(18 + x) - 24(18 - x)}{(18 - x) (18 +x)} = 1 \\\\\\:\implies\sf \dfrac{24( \:\cancel{18} + x - \:\cancel{18} + x}{(18 - x) (18 +x)} = 1 \\\\\\:\implies\sf \dfrac{24(2x)}{324 - x^2} = 1\\\\\\:\implies\sf 324 - x^2 = 48x\\\\\\:\implies\sf -x^2 - 48x + 324 = 0\\\\\\:\implies\sf x^2 + 48x - 324 = 0\\\\\\:\implies\sf x^2 - 6x + 54x - 324 = 0\\\\\\:\implies\sf x(x - 6) +54(x - 6) = 0\\\\\\:\implies\sf (x -6) (x + 54) = 0\\\\\\:\implies{\underline{\boxed{\frak{\purple{ x = 6 \: and \: -54}}}}}\:\bigstar$

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Ignoring negative value, because speed can't be negative.

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$\therefore\:{\underline{\sf{Hence, \: speed \: of \ the \: stream \: is\: \bf{6 km/hr}.}}}$