# 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

• How many webs does Spiderman's web shoot in one minute? Or do you mean "after 90km" rather than "after using 90 webs"? – Astralbee Aug 29 '19 at 9:02
• What is "magic control"? Does it only happen once? – Astralbee Aug 29 '19 at 9:03
• @magic control means you need to spend 10 minutes to control the broomstick – Sayed Mohd Ali Aug 29 '19 at 9:04
• @Astralbee 1 web will give swing upto 2km. I will edit that part... – Sayed Mohd Ali Aug 29 '19 at 9:05
• @Astralbee every defect will activate again after completing the mentioned time... – Sayed Mohd Ali Aug 29 '19 at 9:15

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

• You didn't consider the combinations. – Mohit Jain Aug 29 '19 at 9:22
• @MohitJain I didn't, but ALL of Rabbit's magical items make him SLEEP for a fixed time, so if he's asleep he can't switch to another item until he wakes up. His fastest item is the time machine, after he's slept for 30 mins he should continue using that, not anything slower. I still think it's Turtle to win. – Astralbee Aug 29 '19 at 9:44
• Maybe your final answer is correct. My point is what if a competitor uses magical item for 200 - delta km if that item makes him sleep after 200 km? – Mohit Jain Aug 29 '19 at 9:57
• @MohitJain All my calculations involve using the one item for the full race. Turtle has an item that will cover the entire race at the fastest speed (3km per hour). No other item is faster. It also only involves only 1 delay of 10 minutes - no other item has a shorter delay except the web (5 minutes) but that delay will occur more than once. You don't really have to do the maths to see that its one item to win. – Astralbee Aug 29 '19 at 10:01
• I think Mohit's quesiton is what if rabbit teleported for 198km, then used the time machine for 302. He'd only have to sleep once. However, that'd still take about 242 minutes, which is slower than using the time machine the whole way. The issue is that the time machine, with sleeping, is faster than the teleporter without. – user3294068 Sep 6 '19 at 13:41