Answer :
Answer:
Speed of the boat=36 km/h
Speed of the current=4 km/h
Step-by-step explanation:
We have the following data:
[tex]V_{c}=\frac{160 km}{4 h}=40 km/h[/tex] is the speed of the boat traveling with the current
[tex]V_{a}=\frac{160 km}{5 h}=32 km/h[/tex] is the speed of the boat traveling against the current
From here we can write two equations:
[tex]V_{c}=V_{b}+V_{current}[/tex] (1)
[tex]V_{a}=V_{b}-V_{current}[/tex] (2)
Where [tex]V_{b}[/tex] is the speed of the boat and [tex]V_{current}[/tex] is the speed of the curent
Adding both equations, we have:
[tex]V_{c}+V_{a}=2V_{b}[/tex] (3)
Isolating [tex]V_{b}[/tex]:
[tex]V_{b}=\frac{V_{c}+V_{a}}{2}[/tex] (4)
[tex]V_{b}=\frac{40 km/h+32 km/h}{2}[/tex] (5)
[tex]V_{b}=36 km/h[/tex] (6) This is the speed of the motorboat
Now, substituting (6) in (1):
[tex]40 km/h=36 km/h+V_{current}[/tex] (7)
Finding [tex]V_{current}[/tex]:
[tex]V_{current}=4 km/h[/tex] (8) This is the speed of the current