My Math Forum  

Go Back   My Math Forum > High School Math Forum > Pre-Calculus

Pre-Calculus Pre-Calculus Math Forum


Thanks Tree1Thanks
Reply
 
LinkBack Thread Tools Display Modes
March 3rd, 2018, 01:45 AM   #1
Newbie
 
Joined: Mar 2018
From: poland

Posts: 2
Thanks: 0

How to solve this problem? (HARD)

A giant rabbit is tied to a pole in the ground by an infinitely stretchy elastic cord attached to its tail. A hungry flea is on the pole watching the rabbit. The rabbit sees the flea, jumps into the air and lands one kilometre from the pole (with its tail still attached to the pole by the elastic cord). The flea gives chase and leaps into the air landing on the stretched elastic cord one centimetre from the pole. The rabbit, seeing this, again leaps into the air and lands another kilometre away from the pole (i.e., a total of two kilometres from the pole). Undaunted, the flea bravely leaps into the air again, landing on the elastic cord one centimetre further along. Once again the rabbit jumps another kilometre and the flea jumps another centimetre along the cord. If this
continues indefinitely, will the flea ever catch up to the rabbit? (Assume the earth is flat and extends infinitely far in all directions.)
mansmath is offline  
 
March 3rd, 2018, 04:41 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 18,962
Thanks: 1606

Yes.
skipjack is offline  
March 3rd, 2018, 07:37 AM   #3
SDK
Senior Member
 
Joined: Sep 2016
From: USA

Posts: 379
Thanks: 205

Math Focus: Dynamical systems, analytic function theory, numerics
In the limit they will be $-\frac{1}{12}$ meters apart.
SDK is offline  
March 3rd, 2018, 07:54 AM   #4
Newbie
 
Joined: Mar 2018
From: poland

Posts: 2
Thanks: 0

Thank you, but If could I ask you, HOW did you solve it?
mansmath is offline  
March 3rd, 2018, 08:31 AM   #5
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 1,944
Thanks: 1011

Quote:
Originally Posted by SDK View Post
In the limit they will be $-\frac{1}{12}$ meters apart.
a negative length?
romsek is offline  
March 3rd, 2018, 01:14 PM   #6
Global Moderator
 
Joined: Dec 2006

Posts: 18,962
Thanks: 1606

It's an easy question, but first consider what happens if the rabbit leaps a much shorter distance, such as 2 cm. Bear in mind that once the flea is on the elastic, it moves as the elastic is stretched by the rabbit's leap.
Thanks from topsquark
skipjack is offline  
May 7th, 2018, 02:17 PM   #7
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,165
Thanks: 867

Quote:
Originally Posted by mansmath View Post
A giant rabbit is tied to a pole in the ground by an infinitely stretchy elastic cord attached to its tail. A hungry flea is on the pole watching the rabbit. The rabbit sees the flea, jumps into the air and lands one kilometre from the pole (with its tail still attached to the pole by the elastic cord). The flea gives chase and leaps into the air landing on the stretched elastic cord one centimetre from the pole.
So after one jump the rabbit is 999.98 meters away from the flea.

Quote:
The rabbit, seeing this, again leaps into the air and lands another kilometre away from the pole (i.e., a total of two kilometres from the pole).
So the cord has doubled in length. The flea, that was 1 cm from the pole is now 2 cm from the pole.
Quote:
Undaunted, the flea bravely leaps into the air again, landing on the elastic cord one centimetre further along.
The flea is now 3 cm from the pole and the rabbit is 1999.97 meters from the flea.

Quote:
Once again the rabbit jumps another kilometre and the flea jumps another centimetre along the cord.
The cord has stretched by 3/2 so, before the jump the flea was 9/2= 4.5 cm from the pole and after jumping one cm. is 5.5 cm from the pole, 2994.5 m from the rabbit.
Quote:
If this
continues indefinitely, will the flea ever catch up to the rabbit? (Assume the earth is flat and extends infinitely far in all directions.)
The sequence is 999.8, 1999.97, 2994.5, etc. No, that is NOT converging to 0.
Country Boy is offline  
May 8th, 2018, 04:16 AM   #8
Global Moderator
 
Joined: Dec 2006

Posts: 18,962
Thanks: 1606

If you obtain a formula for those distances, you'll see that the flea does eventually catch up.
skipjack is offline  
May 8th, 2018, 07:34 PM   #9
SDK
Senior Member
 
Joined: Sep 2016
From: USA

Posts: 379
Thanks: 205

Math Focus: Dynamical systems, analytic function theory, numerics
I think CountryBoy is not assuming that each jump made by the rabbit stretches the elastic cord and causes the flea to move further away from the pole. This happens in addition to the distance traveled by the flea.

His analysis is correct within that interpretation. However, I think this is not the interpretation intended. Math is precise for a reason, though rarely is that reason so transparent as attempting to get inside the mind of a random internet crazy person to determine what they mean when they say a rabbit leaps 1km.
SDK is offline  
May 8th, 2018, 08:24 PM   #10
Global Moderator
 
Joined: Dec 2006

Posts: 18,962
Thanks: 1606

Country Boy stated "So the cord has doubled in length. The flea, that was 1 cm from the pole is now 2 cm from the pole." Hence the flea's movement due to the cord being stretched by the rabbit is being taken into account. This is an old puzzle.
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Pre-Calculus

Tags
animal, hard, problem, solve



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Nice hard equation to solve - can you do it? victoriamath Algebra 13 August 11th, 2014 08:48 AM
solve the following equation - Hard problem mjbecnel Algebra 7 March 5th, 2014 03:50 AM
solve the following equation - Hard problem mjbecnel Complex Analysis 4 March 4th, 2014 01:47 PM
Please help me to solve this. It's really hard. jiasyuen Algebra 7 September 30th, 2013 06:38 PM
A hard system of equations to solve Obsessed_Math Algebra 4 February 23rd, 2012 06:03 AM





Copyright © 2018 My Math Forum. All rights reserved.