Respuesta :
Answer:
The speed of the boat in still water is 12km/h.
Explanation:
This is a relative motion problem. The boat is moving relative to the water, which is moving relative to the ground. We can express this with the formula:
[tex]v_{b/0}=v_{b/w}+v_{w/0}[/tex]
Where [tex]v_{b/0}[/tex] is the speed of the boat relative to the ground, [tex]v_{b/w}[/tex] is the speed of the boat relative to the water, and [tex]v_{w/0}[/tex] is the speed of the water relative to the ground.
We have that [tex]v_{w/0}=8km/h[/tex] and that, in the first trip [tex]v_{b/0}=\frac{x}{2h}[/tex] and in the second trip [tex]v_{b/0}=\frac{x}{10h}[/tex], where x is the distance traveled. Also, in the first trip [tex]v_{b/w}[/tex] and [tex]v_{b/0}[/tex] are positive and in the second one are negative (because the boat goes in opposite directions). So, using some mathematics, we can say that:
[tex]\frac{x}{2h} =v_{b/w}+8km/h; -\frac{x}{10h} =-v_{b/w}+8km/h\\\\x=2h(v_{b/w}+8km/h);x=-10h(-v_{b/w}+8km/h)\\\\\implies 2h(v_{b/w}+8km/h)=-10h(-v_{b/w}+8km/h)\\\\-4v_{b/w}=-48km/h\\\\v_{b/w}=12km/h[/tex]
This means that the speed of the boat relative to the water is 12km/h. This is independent to the speed of water, so the speed of the boat in still water is 12km/h.
