Question

a boat on the Potomac River travels the same distance downstream in 2/3 hour as it does going upstream in 1 hour. If the speed of the current is 3 mph, find the speed of the boat in still water

Answer 1

$\bf \begin{array}{ccccllll} &distance&rate&time(hrs)\\ &-----&-----&-----\\ upstream&d&r-3&\frac{2}{3} \\\\ downstream&d&r+3&1 \end{array}\\\\ -----------------------------\\\\ thus\qquad \begin{cases} d=(r-3)\frac{2}{3} \\\\ d=(r+3)1 \end{cases}\qquad d=d\qquad thus \\\\\\ (r-3)\cfrac{2}{3}=(r+3)1$

notice, the distance is the same, upstream or downstream, thus is "d" for both

solve for "r"