Question

A motorboat takes 5 hours to travel 200 miles going upstream. The return trip takes 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

\(\large{ b=\textit{boat's rate}\qquad s=\textit{stream rate}
\\ \quad \\
\begin{array}{rcccllll}
&distance&rate&time
\\\hline\\
upstream&200&b-r&5\\
downstream&200&b+r&4
\end{array}\implies
\begin{array}{llll}
{\color{brown}{ 200}}=(b-r)5
\\ \quad \\
{\color{brown}{ 200}}=(b+r)4
\end{array}
\\ \quad \\
\implies (b-r)5=(b+r)4}\)

solve for "b" or "r"

then grab that value and substitute on either of the two equations above to get the other variable