Question

A motor boat speed 18km/h in still water take 1hr more to go 24km/hr upstream than to down stream to the same spot find the speed of the stream

Answer 1

Solution:

Given

speed of the boat = 18km/h  

let the speed of stream be x km/hr  

speed of the boat upstream = speed of the boat in still water  - speed of the boat  

speed of the boat upstream = (18-x) km/hr  

speed of the boat downstream = speed of the boat in still water +speed of boat  

speed of the boat downstream = (18+x) km/hr  

time of upstream journey = time for downstream journey   + 1hr  

distance coated by upstream / speed of the boat upstream = distance coated by downstream / speed of the downstream + 1 hour

=> 24/(18-x) = 24/(18+x) +1hr

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

=> 48x=324-$x^{2}$

=> -x² - 48x + 324 = 0

=> x² + 48x - 324 = 0

=> x² - 6x + 54x - 324 = 0

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

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

For the equation to be 0,

⇒ x + 54 = 0 (or) x - 6 = 0

⇒ x = -54 (or) x = 6

X= 6 (the speed of the stream is 6km/hr)

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@GauravSaxena01

Answer 2

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Let the speed of the stream be = x

speed of the motor boat upstream = ( 18-x)

speed of the motor boat for downstream = ( 18+x)

according to statement or QÜËẞTÏØÑ ...

$\frac{24}{18 - x} - \frac{24}{18 + x} = 1 \\ \\ \frac{24(18 + x - 18 + x)}{(18 - x)(18 + x)} = 1 \\ \\ 48x = 324 {x}^{2} \\ \\ {x}^{2} + 45x - 324 = 0 \\ \\ {x}^{2} + 54x - 6x - 324 = 0 \\ \\ (x + 54) - 6(x + 54) = 0\\ \\ (x + 54)(x - 6) = 0 \\ \\ x = - 54 \: \: \: \: \: x = 6$

Rejecting negative value of x because speed cannot be in negative we have x= 6 . Hense , the speed of the stream is 6km/h .
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@MAYA KASHYAP

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