It takes 3 hours to paddle a kayak 12 miles downstream and 4 hours for the return trip upstream. Find the rate of the kayak in still water. Let k= the rate of the kayak in still water and c= the rate of the current.

r t d rt=d
Downstream k+c 3 12 3(k+c)=12
Upstream k − c 4 12 4(k – c)=12

The rate of the kayak in still water is
4
miles per hour.