Answer :
Answer:
The rate of the boat in still water is;
[tex]48\text{ km/h}[/tex]The rate of the current is;
[tex]16\text{ km/h}[/tex]Explanation:
Let x represent the rate of the boat in still water, and y represent the rate of the current;
Speed upstream is;
[tex]x-y[/tex]Speed downstream is;
[tex]x+y[/tex]Recall that distance equals the product of speed and time;
Upstream the product is;
[tex]4(x-y)=128------1[/tex]Downstream;
[tex]2(x+y)=128-------2[/tex]Expand both equation and multiply equation 2 through by 2;
[tex]\begin{gathered} 4x-4y=128--------1a \\ 2x+2y=128 \\ \text{ multiply through by 2;} \\ 4x+4y=256------2a \end{gathered}[/tex]solve the simultaneous equation by elimination; add equation 1a and 2a together;
[tex]\begin{gathered} 4x+4x+4y-4y=128+256 \\ 8x=384 \\ x=\frac{384}{8} \\ x=48 \end{gathered}[/tex]Then we can substitute x into equation equation 2 to get y;
[tex]\begin{gathered} 2(x+y)=128 \\ x+y=\frac{128}{2} \\ y=64-x \\ y=64-48 \\ y=16 \end{gathered}[/tex]Therefore, the rate of the boat in still water is;
[tex]48\text{ km/h}[/tex]The rate of the current is;
[tex]16\text{ km/h}[/tex]