In The Cay, in what chapter did Timothy and Phillip end up on the island?
This happens in Chapter 7.
Because most of the story takes place on the island, we know to look near the beginning of the novel to find out exactly when these two main characters ended up there. But if you recall, the adventure didn't start immediately--Phillip was living at home, with his mother and father, before they set out on the journey.
We saw Phillip and his mom board the S. S. Hato at the end of Chapter 2 and set sail.
Things start getting really exciting in Chapter 3, when the torpedo hits the ship and Phillip tries to stay with his mother but gets knocked unconscious by something--and that's when he wakes up on the raft with Timothy. All they can see around them is open sea.
Chapter 4 opens with both of these characters still floating on the raft, but most of that chapter deals with Phillip realizing that he's becoming blind.
Chapter 5 gives Timothy and Phillip a false hope of rescue when they hear an aircraft.
And as Chapter 6 begins, Timothy spots an island in the distance. He describes it as very small, "outrageous low," and about two miles away from their raft.
In Chapter 7, Timothy then risks the possibly shark-infested waters and kicks the raft to shore. The two characters are safer here than in the open sea in the raft--but there's no one around, and no way to call for help. The adventure is really starting now.