A worm is crawling on an elastic band that is 20 inches long. Eachday the worm crawls 1 inch. Each evening, a boy stretches the band 10 inches (moving the worm some too). Does the worm ever reach the end of the band? If so, how long does it take him? If not, why not?
1dont [17][17][17].......be [1][1][1]...celestine........[9][9][9]...............
1Please tell me if I am making a mistake.
The distance moved by worm in 1 day = 1inch
String length after 1 day = 30 inches
This increases distance betwwen any two points on string increases to 30/20 times original.
So distance moved by worm in 1st day is 3/2 inches.
So the following algorithm can be made
(d(n-1) + 1) (n+2) / (n+1) = dn where dn denotes distance moved by the nth day.
How do I solve this.
13Ans is COOL[4]
[e10]=22026 days
assume:worm has a life of more than 60 years!!!![3]
9hint
ans comes in exponential terms
try forming a integrable eq
13bhaiya...is this physics or mathematics....[12]
then i ve done a mistake putting it here[3]
62No this is not a riddle gaurav.
Infact a classical question of physics
1Initially the worm is at one end of the string. In one day it moves 1 inch. Then the boy increases the length to 30 inches.
That is he increases distance between 2 points on the string to 3/2 times original distance.
Then Distance moved by worm is 3/2 inches. After 1 more day, the distance moved becomes (3/2 + 1) = 5/2 inches. Then the boy increases length to 40 inches.
Effectively increasing distance between 2 points to 4/3 times original. Now the worm has moved (4/3)(5/2) = 10/3 inches.
Percentage distance moved by worm in 1st day = {(3/2)/30 } 100 = 5%
percentage distance moved in 2nd day = {(10/3)/40} 100 = 8.33%
percentage distance moved in 3nd day = 10.83%
It is increasing therefore sometime it must become 100% Trying out the time taken now.
1Do we assume that the elastic band will not break . (There are some stupid riddles which have such answers )
62This was posted by Rohan long back..
my mistake I messed with the database that day and it got deleted
skygirl had posted the solution to this one..
Answer is yes..
1Elastic Materials can regain itz original configuration after it is streched...so definitely the worm will reach the other end.........
62This is a classic question, very very famous..
I guess I will put this to the QOD...
Can someonetry this?
