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A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.
Given: A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot
To do: To find the speed of the stream.
Solution:
Let the speed of the stream be s km/h.
Speed of the motor boat 24 km/h
Speed of the motor boat upstream $( 24\ –\ s)$
Speed of the motor boat downstream $24+s$
According to the given condition,
$\frac{32}{24-s} -\frac{32}{24+s} =1$
$\Rightarrow 32\left(\frac{1}{24-s} -\frac{1}{24+s}\right) =1$
$\Rightarrow 32\left(\frac{24+s-24+s}{576-s^{2}}\right) =1$
$\Rightarrow 32\left(\frac{2s}{576-s^{2}}\right) =1$
$\Rightarrow 64s=576-s^{2}$
$\Rightarrow s^{2} +64s-576=0$
$\Rightarrow s^{2} +72s-8s-576=0$
$\Rightarrow s( s+72) -8( s+72) =0$
$\Rightarrow ( s-8)( s+72) =0$
If $s-8=0$
$\Rightarrow s=8$
If $s+72=0$
$\Rightarrow s=-72$
Since, Speed of the stream can't be negative, the speed of the stream is $8\ km/h$.
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