Worm Crawls

A rubber string is 10 meters long. A worm crawls from one end to the other at 1 meter/hr. After each hour the string stretches to become 1 meter longer than it's last length.Will it reach the end ?

Solution

Yes, the worm will reach the end because at the end of every hour when rubber band stretches, the distance travelled by the worm in past hr(s) will also increase and remaining distance to travel becomes less as compared to earlier.

For exapmle:
at the end of 1st hour:
worm has tarvelled: 1meter

Now, when the whole length of rubber band becomes 11m then effective distance travelled by the worm in past 1hr becomes 1.1 merter.

if we calculate remaining distance to travel: 11 - 1.1 = 9.9 meters

Clearly it has reduced from 10 metres.