Question

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

Answer 1

Hey there ,

as per your question

Let the speed of the stream be = x km/hr

Speed upstream = ( 18-x)km/hr

Speed downstream = ( 18+x)km/hr

Time taken to cover 24 km upstream = 24/(18-x) hrs

Time taken to cover 24 km downstream = 24/(18+x) km/hr

Equation is as follows :

24/(18-x) = 24/(18+x). +. 1

24/(18-x). =. (42+x)/(18+x)

24(18+x). =. (42+x)(18-x)

432+24x. =. 756 - 42x. +18x - x^2

x^2. + 48x. -324 = 0

Using Quadratic formula : x= (-b. +-. √ (b^2 - 4ac))/2a

Substitute the value according the above equation : (a= 1 ,b= 48 ,c= -324)

The answer will be : x= 6 and -54 ( neglecting )

Hence the speed of the stream is 6 km/hr

If it helps ,please mark it as BRAINLIEST

Thank You

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