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# A steamer goes downstream and covers the distance between two ports in $4$ hour, while it covers the same distance upstream in $6$ hours. If the speed of the stream is $2\ km/h$, find the speed of the steamer in still water.

**Given:**A steamer goes downstream and covers the distance between two ports in $4$ hour, while it covers the same distance upstream in $6$ hours. The speed of the stream is $2\ km/h$.

**To do:**To find the speed of the steamer.

**Solution:**

Let the speed of the steamer in still water be $x\ km/h$.

Then, the speed downstream $=(x+2)\ km/h$

and the speed upstream $=(x-2)\ km/h$

Given, distance covered in $4$ hours downstream = distance covered in $6$ hours upstream

$\because 4( x+2)=6( x-2)$ [$\because distance=speed\times time$]

$\Rightarrow 4x+8=6x-12$

$\Rightarrow 4x-6x=-12-8$

$\Rightarrow -2x=-20$ or $x=\frac{20}{2}=10\ km/h$

Thus, the speed of the steamer is $10\ km/h$.

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