mathematics - Magic Race between Rabbit and Turtle - who will win?

The race is for 500km and these are the following items they can use in the magic race... Every defect will activate again after completing the mentioned time.

Rabbit has the following items available:

1. 
   

   Teleportation by Decepticons.
   speed: 2km/min
   defect: makes you sleep for 20 minutes after traveling 200km

   
   


2. 
   

   Sitting on Aladdin’s magic carpet.
   
   speed: 1km/min
   defect: makes you sleep for 5 minutes after traveling 100km

   
   


3. 
   

   Doraemon’s Time Machine.
   speed: 3km/min
   defect: makes you sleep for 30 minutes after traveling 200km

   
   

Turtle has the following items available:

1. 
   

   Spiderman’s web.
   speed: 2km/min
   defect: you will lose all webs for 5 minutes after using 90, 1 web is limited to give 2km swing

   
   


2. 
   

   Harry Potter’s broomstick.
   speed: 3km/min
   defect: you need to spend 10 minutes on magic control before riding on it. And magic control means to control the broomstick before riding it

   
   
   


3. 
   

   Doraemon's anywhere door.
   speed: 2km/min
   defect: it will increase distance 10km after covering 200km

   
   

Answer

I think the answer is:

Turtle will win. Using Harry Potter's broomstick he can make the entire 500km run in 176.6 mins (10 minutes "control", then the full 500km at 3km per hour is just over 166.6 mins). Rabbit can't win with any combination of his items as they all have the defect of making him sleep, so he can't use one item after the other until he's woken up. His best bet is to stick with the fastest item and that still only gets him there in 226 minutes.

This is because:

- Teleportation by Decepticons. { speed: 2km/min } { defect: make you sleep for 20minutes after traveling 200km } takes 290mins

- Sitting on Alladin’s magic blanket. { speed: 1km/min } { defect: make you sleep for 5 minutes after 100km } 525minutes

- Doremon’s Time Machine. { speed: 3km/min } { defect: make you sleep for 30 minutes after traveling 200km } 226mins

- Spiderman’s web. { speed: 2km/min } { defect: you will lose all webs for 5 minutes after using 90 } 275mins

- Harry Potter’s broomstick. { speed: 3km/min } { defect: you need to spend 10 minutes on magic control before riding on it. } 176mins

- Doremon's anywhere door. { speed: 2km/min } { defect: it will increase distance 10km after covering 200km } 260minutes