Answered

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A man can row a boat at 4kmhr in still water. He rows the boat 2km upstream and 2 km back to his starting place in 2 hours. How fast is the stream flowing

Sagot :

lublana

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

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