A boat takes 4 hours to travel from a place X to Y downstream and back from Yto X upstream.If the distance from X to Y is 10.5 km, and the speed ofthe current is 9 km/h, then the speed of the boat in still water, in km/h is:

As per the given question,

time =4 hour

distance =10.5 km

Speed of the stream =9km/hour

Let the speed of the boat in the calm water =v

So, $$t=t_1+t_2$$

$$\Rightarrow 4=\dfrac{10.5}{v+9}+\dfrac{10.5}{v-9}$$

$$\Rightarrow 4=10.5 \dfrac{v-9+v+9}{(v-9)(v+9)}$$

$$\Rightarrow 4=10.5 \dfrac{2v}{(v-9)(v+9)}$$

$$\Rightarrow 4v^2-81\times 4=21v$$

$$\Rightarrow 4v^2-21v-324=0$$

$$\Rightarrow 4v^2-48v+27v-324$$

$$\Rightarrow 4v(v-12)-27(v-12)=0$$

$$\Rightarrow (v-12)(4v-27)=0$$

Hence, v=12 km/hour.