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

Let's first calculate the upstream and downstream speeds of the boat:
$$\text{Upstream Speed }(v_u)=\frac{\text{Distance}}{\text{Time}}=\frac{80\text{ km}}{16\text{ hours}}=5\text{ km/hour}$$

$$\text{Downstream Speed }(v_d)=\frac{\text{Distance}}{\text{Time}}=\frac{72\text{ km}}{12\text{ hours}}=6\text{ km/hour}$$

The formula for the speed of a boat in still water ($v_b$) is the average of its downstream and upstream speeds:

$$v_b=\frac{v_d+v_u}{2}$$

$$v_b=\frac{6+5}{2}=\frac{11}{2}=5.5\text{ km/hour}$$