A boat takes a total of 2 hours to cover 9 km downstream and return, given that the speed of the stream is 6 km/h. What is the speed of the boat in still water?

Let's assume the speed of the boat in still water and the speed of the stream is 'B' and 'C' respectively.

A boat takes a total of 2 hours to cover 9 km downstream and return, given that the speed of the stream is 6 km/h.

$$\frac{9}{B+C}+\frac{9}{B-C}=\ 2$$

$$\frac{9}{B+6}+\frac{9}{B-6}=\ 2$$

$$\frac{9\left(B-6\right)+9\left(B+6\right)}{B^2-6^2}=\ 2$$

$$\frac{9B-54+9B+54}{B^2-36}=\ 2$$

$$\frac{18B}{B^2-36}=\ 2$$

$$\frac{9B}{B^2-36}=\ 1$$

$$B^2-\left(12-3\right)B-36=0$$

$$B^2-12B+3B-36=0$$

$$\left(B-12\right)\ \left(B+3\right)=0$$
B = 12, -3

The negative value of 'B' is not possible here.

So the speed of the boat in still water = B = 12 km/h