Let x mi/h be the speed of the boat in still water and y mi/h be the speed of stream.
1) Downstream.
The speed of the boat travelling downstream is x+y mi/h. Then
[tex](x+y)\cdot 10=280.[/tex]
2) Upstream.
The speed of the boat travelling upstream is x-y mi/h. Then
[tex](x-y)\cdot 20=280.[/tex]
3) Solve the system of equations:
[tex]\left\{\begin{array}{l}(x+y)\cdot 10=280\\ \\(x-y)\cdot 20=280\end{array}\right.\Rightarrow \left\{\begin{array}{l}x+y=28\\ \\x-y=14\end{array}\right..[/tex]
Add these two equations:
[tex]x+y+x-y=28+14,\\ \\2x=42,\\ \\x=21\text{ mi/h}.[/tex]
Subtract these two equations:
[tex]x+y-x+y=28-14,\\ \\2y=14,\\ \\y=7\text{ mi/h}.[/tex]
Answer: the speed of the boat in still water is 21 miles per hour and the speed of the stream is 7 miles per hour.
