Answer:
2.83km/hr
Explanation:
Let stream flowing at the rat x km/hr
In still water
Speed of boat=4km/hr
Upstream speed=4-x
Downstream speed=4+x
Total time=2 hr
Time=Distance/speed
According to question
[tex]\frac{2}{4+x}+\frac{2}{4-x}=2[/tex]
[tex]\frac{8-2x+8+2x}{(4+x)(4-x)}=2[/tex]
[tex]\frac{16}{4^2-x^2}=2[/tex]
Using the formula
[tex](a+b)(a-b)=a^2-b^2[/tex]
[tex]4^2-x^2=\frac{16}{2}[/tex]
[tex]16-x^2=8[/tex]
[tex]16-8=x^2[/tex]
[tex]8=x^2[/tex]
[tex]x=\sqrt{8}=2.83km/hr[/tex]
Hence, the stream is flowing at 2.83km/hr
