Question

a man can row about 4kmperhr in a still water.he rows the boat 2km up the stream and 2km back to his starting point in 2hr.how fast is the stream flowing. ​

Answer 1

Answer:

The stream flowing  at a speed of $2.828 \mathrm{km} / \mathrm{hr}$

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,  

$2=\left(\frac{2}{4-x}\right)+\left(\frac{2}{4+x}\right)$

$2=\frac{2(4+x)+2(4-x)}{(4-x)(4+x)}$

$2(4-x)(4+x)=2(4+x)+2(4-x)$

$2(4-x)(4+x)=2(4+x+4-x)$

By cancelling 2 on both sides,

$16-x^{2}=8$

$x^{2}=16-8=8$

$x=\sqrt{8}$

$x=2.828 \mathrm{km} / \mathrm{hr}$

Result:

Thus the speed of the stream is $2.828 \mathrm{km} / \mathrm{hr}$