[tex] \large \mathcal{ANSWER:} [/tex]
[tex] \large \boxed{13.75\:\textsf{mph}} [/tex]
[tex] \large \mathcal{SOLUTION:} [/tex]
[tex] \begin{array}{l} \textsf{Let}\:s\:\textsf{be the speed of Shannie in still water.} \\ \\ \quad \quad \quad \begin{aligned} \quad \textsf{Time} &= \dfrac{\textsf{Distance}}{\textsf{Speed}} \\ \textsf{T}_{\textsf{downstream}} &= \textsf{T}_{\textsf{upstream}} \\ \dfrac{15}{s + 5} &= \dfrac{7}{s - 5} \end{aligned} \\ \textsf{where:} \\ \begin{aligned} \quad s + 5 &= \textsf{downstream speed \footnotesize (with the current)} \\ s - 5 &= \textsf{upstream speed \footnotesize (against the current)} \end{aligned} \\ \\ \textsf{Solving for}\: s,\\ \quad \begin{aligned} 15(s - 5) &= 7(s + 5) \\ 15s - 75 &= 7s + 35 \\ 15s - 7s &= 35 + 75 \\ 8s &= 110 \\ s &= \dfrac{110}{8} \\ \implies s &= \boxed{13.75\:\textsf{mph}} \end{aligned} \end{array} [/tex]
[tex] \texttt \color{cyan} {\#CarryOnLearning} [/tex]
