SOLUTION: A strip of paper 4 inches long is given a half twist and the ends are joined to form a Mobius strip. If a beetle lands on the paper and starts walking, how far does it walk before

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A strip of paper 4 inches long is given a half twist and the ends are joined to form a Mobius strip. If a beetle lands on the paper and starts walking, how far does it walk before      Log On


   

Question 975353: A strip of paper 4 inches long is given a half twist and the ends are joined to form a Mobius strip. If a beetle
lands on the paper and starts walking, how far does it walk before reaching its starting point?
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If the strip had not been cut in half and re-oriented, the beetle would have only needed to make 1 revolution to get back top the starting point.
Since it was re-oriented, the beetle needs to make 2 revolutions to get back to the beginning.
Each revolution is 4 inches so the total distance is 8 inches.

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
8 inches because a strip of paper has TWO sides and he has to walk on BOTH sides
to get back to the point on the side where he started.

Further explanation:

Suppose the beetle starts at the place where the twisted ends were joined.

Then when he walks 4 inches, he will NOT be back to where he started, for he will
be at the point on the OPPOSITE SIDE of the paper from the point he started at. 
Then he will walk another 4 inches and then finally he will be back to the very
point he started at.

Edwin