Answer: [tex]45\ mph[/tex], [tex]5\ mph[/tex]
Step-by-step explanation:
Given
A motorboat takes 5 hours to travel 200 miles upstream and 4 hours to go downstream
Suppose the speed of motorboat in still water and rate of current be x and y respectively.
during upstream
[tex]\Rightarrow 5=\dfrac{200}{x-y}\\\\\Rightarrow x-y=40\quad \ldots(i)[/tex]
During downstream
[tex]\Rightarrow 4=\dfrac{200}{x+y}\\\\\Rightarrow x+y=50\quad \ldots(ii)[/tex]
Add (i) and (ii) we get
[tex]\Rightarrow 2x=90\\\Rightarrow x=45\ mph[/tex]
[tex]\therefore y=5\ mph[/tex]
Thus, the speed of boat in still water is [tex]45\ mph[/tex] and rate of current is [tex]5\ mph[/tex]
