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?

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

The ferry travels 50/60 of the full distance between the island and mainland while Heather swims 10/60 of that distance and they meet.  So, Heather swims at 1/5 the speed of the ferry.  The ferry gets to the mainland 10 minutes after meeting Heather, and at that time Heather has swam for 60 minutes at 1/5 the speed of the ferry.

From the point where the ferry is at the mainland, equate the distance where they meet again at time=t (VF=speed of the ferry).
Heather:  .2*60*VF + .2*VF*t
Ferry:       VF*t

VF cancels and t=15 minutes.  Add the 10 minutes from when they first meet to get the ferry to the mainland, and the answer is 25 minutes.

Edited on December 29, 2024, 12:16 pm

Edited on December 29, 2024, 12:18 pm

Posted by Kenny M on 2024-12-29 12:15:58