Let vb be the velocity of the motorboat and let vs be the velocity of the stream.
We know that when she drives upstream the velocity is 8 m/s, in this scenario the velocities point in opposite directions, then we have the equations:
[tex]v_b-v_s=8[/tex]When she drives downstream the velocites point in the same direction then we have the equation:
[tex]v_b+v_s=12[/tex]hence we have the system of equations:
[tex]\begin{gathered} v_b-v_s=8 \\ v_b+v_s=12 \end{gathered}[/tex]Solving the first equation for the velocity of the boat we have:
[tex]v_b=8+v_s[/tex]Plugging this in the second equation we have:
[tex]\begin{gathered} 8+v_s+v_s=12 \\ 2v_s=4 \\ v_s=\frac{4}{2} \\ v_s=2 \end{gathered}[/tex]Therefore, the velocity of the stream is 2 m/s
