### Brain Teasers

# The Froopaloop Island Ferry

Every two hours, a ferry leaves Froopaloop Island and heads due east to the mainland, taking exactly one hour. Then it leaves the mainland and heads due west back to the island, again taking exactly one hour. Then it repeats.

Instead of taking the ferry to Froopaloop Island, Heather prefers to do something very risky: she dons her gorgeous white bikini and swims to the island. (The inhabitants of the island don't know what she looks like with clothes on.)

One day, Heather left the mainland terminal at exactly the same time the ferry left the island terminal. Exactly 50 minutes later, the ferry passed her.

Assuming both Heather and the ferry travel at a constant speed, and ignoring the time the ferry spends at the mainland terminal, how much time passed between the ferry passing Heather in the opposite direction and passing her in the same direction?

Instead of taking the ferry to Froopaloop Island, Heather prefers to do something very risky: she dons her gorgeous white bikini and swims to the island. (The inhabitants of the island don't know what she looks like with clothes on.)

One day, Heather left the mainland terminal at exactly the same time the ferry left the island terminal. Exactly 50 minutes later, the ferry passed her.

Assuming both Heather and the ferry travel at a constant speed, and ignoring the time the ferry spends at the mainland terminal, how much time passed between the ferry passing Heather in the opposite direction and passing her in the same direction?

### Hint

Fifty minutes after leaving the island terminal, the ferry will go in the opposite direction of Heather.### Answer

Twenty-five minutes passed.When the ferry first passes Heather, it still has 10 minutes to reach the mainland, which means it can travel the same distance in 10 minutes that Heather can in 50 minutes, and therefore is 5 times as fast.

If the distance between the two terminals is x, and the distance Heather has travelled when the ferry passes her the second time is y, then the distance the ferry would have travelled at that time is x+y. Therefore, x+y=5x, which means that y=4x. Since x takes 60 minutes for the ferry, y must take 15 minutes, and x+y must take 75 minutes.

Therefore, the time between Heather leaving the mainland and the ferry passing her for the second time is 75 minutes, and the time between the first and second times the ferry passed her is 75-50, or 25, minutes.

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