Answer:
The stream flowing at a speed of [tex]2.828 \mathrm{km} / \mathrm{hr}[/tex]
Explanation:
Given:
Distance = 2km (both in upstream and downstream)
The speed in still water be x km/hr.
The speed in upstream = 4-x
Speed in downstream = 4+x
Solution:
We know that, Speed = distance/time
So, Time = distance/speed
Therefore,
[tex]2=\left(\frac{2}{4-x}\right)+\left(\frac{2}{4+x}\right)[/tex]
[tex]2=\frac{2(4+x)+2(4-x)}{(4-x)(4+x)}[/tex]
[tex]2(4-x)(4+x)=2(4+x)+2(4-x)[/tex]
[tex]2(4-x)(4+x)=2(4+x+4-x)[/tex]
By cancelling 2 on both sides,
[tex]16-x^{2}=8[/tex]
[tex]x^{2}=16-8=8[/tex]
[tex]x=\sqrt{8}[/tex]
[tex]x=2.828 \mathrm{km} / \mathrm{hr}[/tex]
Result:
Thus the speed of the stream is [tex]2.828 \mathrm{km} / \mathrm{hr}[/tex]
