Traveler's ground speed against the walkaway:
[tex]v_{\text{against}}=4\text{ ft/s}[/tex]Traveler's ground speed with the walkaway:
[tex]v_{\text{with}}=8\text{ ft/s}[/tex]When the traveler is moving against the walkaway, the resulting speed is:
[tex]v_{\text{against}}=|v_{\text{walkaway}}-v_{\text{traveler}}|[/tex]Where v_walkaway is the speed of the walkaway, and v_traveler is the traveler speed off the walkaway.
Similarly, if the traveler is moving with the traveler:
[tex]v_{\text{with}}=v_{\text{walkaway}}+v_{\text{traveler}}[/tex]Then, the system of equations:
[tex]\begin{gathered} 8=v_{\text{walkaway}}+v_{\text{traveler}} \\ 4=v_{\text{walkaway}}-v_{\text{traveler}} \end{gathered}[/tex]Adding these equations:
[tex]\begin{gathered} 8+4=v_{\text{walkaway}}+v_{\text{traveler}}+v_{\text{walkaway}}-v_{\text{traveler}} \\ 2v_{\text{walkaway}}=12_{} \\ v_{\text{walkaway}}=6\text{ ft/s} \end{gathered}[/tex]Using this value and the first equation:
[tex]\begin{gathered} v_{\text{walkaway}}+v_{\text{traveler}}=8 \\ \Rightarrow v_{\text{traveler}}=2\text{ ft/s} \end{gathered}[/tex]