A boat traveled 240 miles downstream, then 240 miles back up stream. The trip downstream took 20 hours. The trip back up stream took 60 hours.The speed of the boat in still water is ______ miles per hour.The speed of the current is ______ miles per hour.

Answer:The speed of the boat in still water is 8 miles per hour.The speed of the current is 4 miles per hour.Step-by-step explanation:Let x mph be the speed of the boat in still water and y mph be the speed of the current.A boat traveled 240 miles downstream, it took him 20 hours. Tavelling downstream, the current "helps" and the speed of the boat is x + y mph. Thus,[tex]20(x+y)=240[/tex] A boat traveled 240 miles upstream, it took him 60 hours. Tavelling downstream, the current "interferes" and the speed of the boat is x - y mph. Thus,[tex]60(x-y)=240[/tex] Solve the system of two equations:[tex]\left\{\begin{array}{l}20(x+y)=240\\60(x-y)=240\end{array}\right.\Rightarrow \left\{\begin{array}{l}x+y=12\\x-y=4\end{array}\right.[/tex]Add these two equations:[tex]x+y+x-y=12+4\\ \\2x=16\\ \\x=8\ mph[/tex]Subtract these two equations:[tex]x+y-(x-y)=12-4\\ \\x+y-x+y=8\\ \\2y=8\\ \\y=4\ mph[/tex]