### Brain Teasers

# A Mile in Still Water

Heather dons her gorgeous white string bikini and jumps into a river flowing at a constant rate. Applying a constant force, she swims exactly one mile downstream, taking exactly 10 minutes, and then exactly one mile upstream, taking exactly 15 minutes. How long will it take Heather to swim exactly one mile in still water?

### Hint

It won't take exactly twelve and a half minutes.### Answer

It will take Heather exactly 12 minutes to swim a mile in still water.If it takes Heather exactly 10 minutes to swim one mile downstream, it will take her exactly 15 minutes to swim one and a half miles downstream. So if she swims one and a half miles downstream and then one mile upstream, she will swim two and a half miles in total, swimming upstream half the time and downstream the other half of the time.

Therefore, Heather can swim exactly two and a half miles in still water in exactly 30 minutes, and therefore exactly one mile in exactly 12 minutes.

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