Word Problem.. Please help

[crosscountryrunner]

Afaf, who lives in the South Pacific, is planning a boat trip. Her boat will hold her plus enough food to last 3 weeks. By a strange coincidence, several small islands about 1 week’s travel apart are near the island he lives on. She plans to travel to the fifth island, which is a large island with grocery stores similar to those on the main island he lives on now. The four small islands in between have no stores and she will not be able to buy any food on those islands. So Afaf realizes that she will have to travel out to an island, store some food, and return to the main island for more supplies. Show how she should organize her food supplies so she can get to the fifth island. How many weeks will his trip take altogether?


To solve this problem I knew that I had to draw the five islands and have enough food on island one to make it to island two and put one on island two then go back to island one for one last trip. She will need to have three weeks worth of food with her when she goes to the fifth island. This being said, I figured out that she would have to have six weeks of food on island one when she takes off for island five. Which would take twelve weeks to get the food to island one, then she will have to have one extra at island two when she leaves there. This being said it will take her 17 weeks to get to island 5.

But this answer is wrong . I got told that she can do it in less then 17 weeks but I don't understand how

 

[Denis]

To island1 and back takes 2 weeks; leaves 1week supply at island1

So after 8 weeks, she has 4week supply at island1, and she's back to main island

She leaves main island (for last time), uses 1week: she now has 6week supply ; we're at the 9 weeks mark

She goes to island2 (3week supply left at island1), leaves 1week at island2, returns to island1 ; 11 weeks so far

Again to island2 (nothing left at island1); so she now has 3week at island2 ; 12 weeks so far

Leaves island2 with the 3weeks: to island 3, to island4, to island5; 15 weeks total