Quandaries & Queries - Math Central

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Question from kishore:

A snail starts crawling from one end along a uniformly stretched elastic band.
It crawls at a rate of 1 foot per minute. The band is initially 10 feet long
and is instantaneously and uniformly stretched an additional 10 feet at the end of each minute.
The snail maintains his grip on the band during the instant of each stretch. At what points in time is the snail
(a) closest to the far end of the band, and
(b) farthest from the far end of the band?

Hi Kishore,

Let's look at the distance from the end after the first minute before the rubber band is stretched:

Now let's look at the distance from the end after the second minute before the rubber band is stretched:

Keep in mind that each minute that passes, the snail gets further away from the end of the rubber band. If you still don't see the answer, try to figure out the distances for a couple more minutes.

Hope this helps,

Janice

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.