Question

Shareen finds that when she drives her motorboat upstream she can travelwith a speed of only 8 m/s, while she moves with a speed of 12 m/s whenshe heads downstream. What is the current of the river on which Shareenis traveling?

Answer 1

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:

$v_b-v_s=8$

When she drives downstream the velocites point in the same direction then we have the equation:

$v_b+v_s=12$

hence we have the system of equations:

$\begin{gathered} v_b-v_s=8 \\ v_b+v_s=12 \end{gathered}$

Solving the first equation for the velocity of the boat we have:

$v_b=8+v_s$

Plugging this in the second equation we have:

$\begin{gathered} 8+v_s+v_s=12 \\ 2v_s=4 \\ v_s=\frac{4}{2} \\ v_s=2 \end{gathered}$

Therefore, the velocity of the stream is 2 m/s