A fisherman can row $2\text{ km}$ against the stream in $20\text{ minutes}$ and return in $15\text{ minutes}$. The speed of the boat in still water is

Let the speed of the boat in still water be $x\text{ km/h}$ and the speed of the stream be $y\text{ km/h}$.
1. Upstream Speed (against the stream):
The fisherman covers $2\text{ km}$ in $20\text{ minutes}=\frac{20}{60}\text{ hours}=\frac{1}{3}\text{ hours}$.

$$\text{Speed upstream }(x-y)=\frac{\text{Distance}}{\text{Time}}=\frac{2}{1/3}=6\text{ km/h}$$

2. Downstream Speed (with the stream, returning):
The fisherman returns covers the same $2\text{ km}$ in $15\text{ minutes}=\frac{15}{60}\text{ hours}=\frac{1}{4}\text{ hours}$.

$$\text{Speed downstream }(x+y)=\frac{\text{Distance}}{\text{Time}}=\frac{2}{1/4}=8\text{ km/h}$$

Adding both equations to solve for the speed of the boat in still water ($x$):

$$(x-y)+(x+y)=6+8$$

$$2x=14⟹x=7\text{ km/h}$$