The worm and the rubber band
A rubber band (well, a rubber string, really) is 10 meters long. There’s a worm that starts at one end and crawls toward the other end, at a speed of 1 meter per hour. After each hour that passes, the rubber string is stretched so as to become 1 meter longer than it just was. Will the worm ever reach the other end of the string?
Also know as – Ant on a rubber rope Puzzle
An ant starts to crawl along a taut rubber rope 1 km long at a speed of 1 cm per second (relative to the rubber it is crawling on). At the same time, the rope starts to stretch uniformly by 1 km per second, so that after 1 second it is 2 km long, after 2 seconds it is 3 km long, etc. Will the ant ever reach the end of the rope?
This is Ant on a rubber rope problem
ANSWER IN SHORT-
The worm will eventually reach the end.
The key to understand this is that the proportion between the total length of the rubber Band and the length walked by the worn can only increase with time, as it will eventually approach one.
EXPLAINATION-
The problem seems impossible because we are looking worm and the rubber Band moving independently.
Things become a little more imaginable – “When we realize that the Worm is on the rubber Band, and the portion of the rubber Band behind the worm also stretches just as the portion in front of the worm does,”
The mathematics are complex, but think of the entire picture of the worm and the rubber Band.
At 0 Hour, the worm is at the very end of the rubber Band, and has 100 percent of the rubber Band in front of it.
At 1 Hour, it’s true that the Worms’s task is considerably increased, but it doesn’t have one hundred percent of the rubber Band in front of it.
And that tiny percentage of the rubber Band that the anworm has traversed will stretch in proportion, just like the rest of the rubber Band.
So, Percentage of distance to be covered is increasing in same proportion to the Distance already covered.
i.e.
Percent of Distance traveled is increasing DIRECTLY PROPORTIONAL to Increase in distance to be traveled.
Your Answer
More puzzles to try-
Wind Blows South and then North
Do you know of a place where the wind blows south and then suddenly shifts direction towards the north?Read More »Apple Division
How do you divide 20 apples into 21 people?Read More »How can you determine which one is magnetized and which is not?
You are in a room with two metal rods and no other metal. One of them is magnetized and the ...Read More »Man shoots himself between his eyes puzzle
A man walks into his bathroom and shoots himself right between the eyes using the real gun with real bullets. ...Read More »Count F Word
Count the number of times the letter “F” appears in the following paragraph: FAY FRIED FIFTY POUNDS OF SALTED FISH ...Read More »Path between natural masses
It is a path situated between high natural masses. Remove it’s first letter & you have a path situated between ...Read More »UPSC number Puzzle – ? + ? + ? + ? + ? = 30
? + ? + ? + ? + ? = 30 You have to fill numbers in place of question ...Read More »Fuel in Car Race Riddle
Before the start of the car race, John and Jacob have the same amount of fuel in their car. With ...Read More »Magical Four Numbers
Find four numbers, the sum of which is 45, so that if 2 is added to the first number, 2 ...Read More »Melanesia and Polynesia
Fiji (in Melanesia) and American Samoa (in Polynesia) are two islands in the South Pacific Ocean. Fiji is about 970 ...Read More »How to marry the princess
A wise king devised a contest to see who would receive the Princess’ hand in marriage. The Princess was put ...Read More »Live in Light
I can only live where there is light, but if light shines upon me, I will die. What am I?Read More »Sheep Mowing grassing riddle
If we tie a sheep to one peg it eats out a circle in grass. If we put a rope ...Read More »Can you spell it riddle
The capital of Turkey is a long word. Can you spell it?Read More »Make 3 squares
Make 3 squares by moving 3 clips only.Read More »Six Faces without Makeup
What has six faces, but does not wear makeup, has twenty-one eyes, but cannot see?Read More »Two Third Cat
Which city is three-fifths chick two third cat and 50% goat?Read More »Make Six Square
In the given figure, you can see that four match sticks are used to form a square. Can you form ...Read More »The famous Monty Hall Problem
You’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind ...Read More »Logical Algebra
Solve the equation by replacing the alphabet with numbers. MOM + MOM + NO = BOOK=Read More »