Samantha swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 12 minutes. If the river flows at 4 mph, how fast can Samantha swim in still water?

Let x be Samatha's speed swimming in still water, such that her speeds swimming upstream and downstream are (x + 4) and (x - 4), respectively. The equations for the time it took her to swim in both directions are shown below,

Upstream: d / (x - 4) = 60 minutes

Downstream: d / (x + 4) = 12 minutes

where d is the distance. Solving for the values of the variables gives x = 6 and d = 120. Thus, Samantha can swim at a rate of 6 mph in still water.