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Steamer covers the distance between two parts in 3 hours when it goes downstream and 5 hours when it goes upstream. Find the speed of the streamer upstream if the stream flows at 3 km per hour.
Given:
Steamer covers the distance between two parts in 3 hours when it goes downstream and 5 hours when it goes upstream.
The stream flows at 3 km per hour.
To do:
We have to find the speed of the streamer upstream.
Solution:
Let the speed of the steamer in still water be $x\ km/h$.
Then, the speed downstream $=(x+3)\ km/h$
and the speed upstream $=(x-3)\ km/h$
According to the question,
Distance covered in $3$ hours downstream $=$ Distance covered in $5$ hours upstream
$\because 3(x+3)=5(x-3)$ [$\because Distance=speed\times time$]
$\Rightarrow 3x+9=5x-15$
$\Rightarrow 5x-3x=9+15$
$\Rightarrow 2x=24$
$\Rightarrow x=\frac{24}{2}=12\ km/h$
Thus, the speed of the steamer is $12\ km/h$.
The speed of the steamer upstream $=12-3=9\ km/hr.$