A bookworm can chew through a millimiter (mm) of paper or cardboard in half an hour. One day it encounters a particularly tasty treat: a two-volume edition of a large book standing on a shelf as shown.

The volumes are identical in size, each has a front and a back cover that is a millimeter thick on each side, and the pages of each are a 10mm thick stack of paper from the first page to the last.

If a bookworm starts its meal on the first page of the first volume (already inside the front cover), how long will it take to eat his way through to the last page of the second volume (inside the second volume’s back cover)?

(In reply to Answer by K Sengupta)

The way the two volumes are placed, the back cover of the 2nd volume and  the front cover of the first volume  touch each other.

Since the worm starts its meal from the inside of the front cover of the 1st volume, the distance to the inside of the back cover of the 2nd volume is precisely 1+1 = 2 mm, and consequently the worm will  take precisely (1/2)*2 = 1 hour to eat his way through to the last page of the second volume  (inside the second volume’s back cover).

 

Posted by K Sengupta on 2008-07-02 12:48:10