There is a rubber band that is looped around an immovable steel rod. It is three inches long. At the fixed end is a spider. He starts walking along the rubber band at the rate of one inch per minute.
A minute after he had started, the rubber band is stretched by three inches. The spider continues walking on it at the same rate.
In another minute, the rubber band is stretched another three inches.
This keeps going on until the spider reaches the end of the rubber band. How long did it take the spider to reach the end?
Answer
10.781355 minutes.
The following shows the lengths of the rubber band, the time in minutes, and the distance travelled by the spider.
3, 0, 0
6, 1, 2
9, 2, 4.5
12, 3, 7.333333
15, 4, 10.41667
18, 5, 13.7
21, 6, 17.15
24, 7, 20.74286
27, 8, 24.46071
30, 9, 28.28968
33, 10, 32.21865
36, 10.781355, 36
