A boat covers a certain distance downstream in 2 hours, while it returns in $2\frac{1}{2}$ hours. If the speed of the current is 3 km/h, what is the speed of the boat in still water?

Let the speed of the boat in still water be $v\text{ km/h}$.Given speed of the current, $c=3\text{ km/h}$.Downstream speed = $v+3$ Upstream speed = $v-3$ Since the distance covered in both directions is equal:
$$\text{Distance}=\text{Downstream Speed}\times \text{Downstream Time}=\text{Upstream Speed}\times \text{Upstream Time}$$
Given Downstream Time = 2 hours and Upstream Time = $2\frac{1}{2}=\frac{5}{2}$ hours:
$$(v+3)\times 2=(v-3)\times \frac{5}{2}$$
$$4(v+3)=5(v-3)$$
$$4v+12=5v-15$$
$$5v-4v=12+15$$
$$v=27\text{ km/h}$$