A boat goes $80\text{km}$ upstream in $16$ hours and $72\text{km}$ downstream in $12$ hours. The speed of the boat in still water is:

Let the speed of the boat in still water be $u\text{km/h}$ and the speed of the stream be $v\text{km/h}$.
1. **Upstream Speed ($u-v$):**
The boat covers $80\text{km}$ upstream in $16$ hours.

$$u-v=\frac{\text{Distance}}{\text{Time}}=\frac{80}{16}=5\text{km/h}\text{— (Equation 1)}$$

2. **Downstream Speed ($u+v$):**
The boat covers $72\text{km}$ downstream in $12$ hours.

$$u+v=\frac{\text{Distance}}{\text{Time}}=\frac{72}{12}=6\text{km/h}\text{— (Equation 2)}$$

To find the speed of the boat in still water ($u$), add Equation 1 and Equation 2:

$$(u-v)+(u+v)=5+6$$

$$2u=11$$

$$u=\frac{11}{2}=5.5\text{km/h}$$