Answer:
V = 1.94 mi/h
Step-by-step explanation:
You can asume that the current helps her when she is downstream and hinders her when she is upstream.
downstream:
[tex]v_T = v + 3[/tex]
upstream:
[tex]v_T=3 - v[/tex]
If v = x / t, then t = x / v thus the time she took to do each part was:
downstream:
[tex]t_d=\frac{7}{3+v}[/tex]
upstream:
[tex]t_u=\frac{7}{3-v}[/tex]
The total time is [tex]t_u+t_d=8[/tex]
Therefore:
[tex]\frac{7}{3-v}+\frac{7}{3+v}=8[/tex]
[tex](7)(3-v)+(7)(3+v)=8(3-v)(3+v)[/tex]
[tex](7)(3-v+3+v)=8(9-v^2)[/tex]
[tex](7)(6)=72-8v^2[/tex]
[tex]42-72=-8v^2[/tex]
[tex]v^2=30/8[/tex]
[tex]v=\sqrt{\frac{30}{8} }[/tex]
v≈1,94
