Question 16709
Let the speed of the boat be x and the speed of the current downstream be y

<pre>

<b>then x+y=27/3=9 km/hr </b>[speed downstream]

<b>then x-y=(2/3*27)/6 </b>[two thirds of distance means 2/3 of 27 km.]
                   <br> [double the time means 6 hours instead of 3]

<b>=2*(18)/6= 6 km/hr</b> [speed upstream]

<br>

<b>now x+y=9
    x-y=6

2x=15 => x=7.5 km/hr </b>[solving simueltanously]

<b>then y=9-x=9-7.5=1.5 km/hr</b>
</pre>
<P>
Hence,speed of boat in still water will be 7.5 km/hr and rate of current is 1.5 km/hr.

Hope this helps,
Prabhat