We know that, when the swimmer swims with the current, he cross the 6 miles in 1.5 hours.
When the swimmer tries to swim against the current, the displacement is zero.
We can conclude two things:
- The resulting speed when he goes with the current is the speed of the swimming plus the speed ot the current.
- When he swims against the current, he can not move forward because the speed of swimming equals the speed of the current.
Then, we can write:
[tex]v_c+v_s=v=\frac{\Delta x}{\Delta t}=\frac{6\text{ miles}}{1.5\text{ hours}}_{}=4\text{ miles/hour}[/tex]vc: speed of the current, vs: speed of the swimming
[tex]\begin{gathered} v_c=v_s=4-v_c \\ 2v_c=4 \\ v_c=v_s=\frac{4}{2}=2\text{ miles/hour} \end{gathered}[/tex]As both speeds are equal, the speed of the current and the speed of the swimming are half the speed of the average speed when swimming with the current.
Answer:
The speed of the current is 2 miles per hour.
