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 Samantha’s speed in still water be v mph and the distance be d miles. Upstream, her speed is v − 4, so d = v − 4 because she swims for one hour. Downstream, 12 minutes is 0.2 hour, so her speed is 5d = v + 4. Substituting d = v − 4 gives 5(v − 4) = v + 4, so v = 6 mph. The correct choice is 6 mph.

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