Respuesta :
Rate of boat in still water is 45 m/h
Rate of current is 5 m/h
Explanation
Step 1
let x represents the spped of the boat
let y represents the rate of the current
hence
A) going upstream
the current is opposite to the movement, so we need to subtract the rate of the current form the rate of the motor boat ,so
[tex]\begin{gathered} sped=(x-y) \\ \text{time}\cdot\text{speed}=dis\tan ce \end{gathered}[/tex]replace
[tex]3\mleft(x-y\mright)=120\rightarrow equation(1)[/tex]B) going downstream
we need to add the rates , so the rate is (x+y)
[tex]\begin{gathered} \text{time}\cdot\text{speed}=dis\tan ce \\ 3(x+y)=150\rightarrow equation(2) \end{gathered}[/tex]Step 2
solve the equations
[tex]\begin{gathered} 3\mleft(x-y\mright)=120 \\ 3\mleft(x+y\mright)=150 \end{gathered}[/tex]divide both side of equation(1) by 3
[tex]\begin{gathered} \frac{3(x-y)}{3}=\frac{120}{3} \\ x-y=40 \\ \text{add y in both sides} \\ x-y+y=40+y \\ x=40+y\rightarrow equation(3) \end{gathered}[/tex]now, divide both sides of the equation (2) by 3 and replace the x value we got previously
[tex]\begin{gathered} 3(x+y)=150 \\ \frac{3(x+y)}{3}=\frac{150}{3} \\ x+y=50 \\ \text{replace the x value} \\ 40+y+y=50 \\ 2y=50-40 \\ y=\frac{10}{2} \\ y=5 \end{gathered}[/tex]finally, replace the y value into equation (3) to know x
[tex]\begin{gathered} x=40+y\rightarrow equation(3) \\ x=40+5 \\ x=45 \end{gathered}[/tex]therefore.
Rate of boat in still water is 45 m/h
Rate of current is 5 m/h
I hope this helps you
