Question 84762

Let the speed of the stream = 'x' km/hr

speed of the boat = 9km/hr

Relative Speed upstream = (9-x) km/hr

Relative speed downstream = (9+x) km/hr

Distance travelled = 12 km up and 12 km down

Time taken for upward journey = distance/speed

                              = 12/(9-x) hrs

 Time taken for downward journey = distance/speed

                              = 12/(9+x) hrs

Total time taken given to be = 3 hrs


==> 12/9-x  + 12/9+x = 3

==> 12(9+x) + 12(9-x) = 3(9+x)(9-x)

==> 108 + 12x + 108 - 12x = 3(81 - x^2)[as (a+b)(a-b) = a^2-b^2)]

==> 216 = 243 - 3x^2

==> 3x^2 = 243 - 216

==> 3x^2 = 27

==> x^2 = 27/3

        = 9

==> x = 3

Thus the speed of the boat = 3 km/hr

Good Luck!!!