Question

A motor boat whose speed is 18 km/hr in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot.find the speed of the steam​

Answer 1

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

Answer 2

Step-by-step explanation:

Given

Speed Of Motor boat water = 18 km / hr

Find :

Speed Of Stream

Solutions :

Let Speed Of stream be X km / hr

Speed Of Water boat in water = 18 km / hr

Upstream Speed = ( 18 - X ) km / hr

Downstream Speed = ( 18 + X ) km / hr

Distance 24 km

Therefore Time taken for upstream = 24/18 - X

Time taken Downstream = 24/18 + X

According to Questions

24/18 - X - 24/18 + X = 1

24 ( 18 + X - 18+X ) / ( 18 - X ) ( 18 + X ) = 1

24 × 2x / 18 ^2 - X ^2 = 1 ( Transposing Digit each other side )

324 - X ^2 = 48 X

X ^ 2 + 48x - 324 = 0 ( Take this type digit Subtract to 48 and Multiple to 324 )

X + 54 X - 6 X -324 = 0

X + 54x - 6x - 324 = 0

X ( X + 54 ) - 6 ( X + 54 ) = 0 ( Take Common X )

( X + 54 ) ( X - 6 ) = 0 ( Take one Positive term and one Negative term )

( X + 54 )

X + 54 = 0

X = - 54

( X - 6 )

X = 0

X = 6

So the Value Positive is always right because Negative value not put So the correct value is Positive value

The Speed Of Stream Value Is 6 km/hr