At my first job out of college a crazy old chemist guy used to test young engineers with various algebra to calculus type problems. We became good friends because I was the only young punk ass engineer who solved his last problem in 5 minutes…
A caterpillar crawls onto an infinitely elastic rubber band.
The initial length of the rubber band is 8 inches.
The inchworm moves forward along the rubber band at a rate of 1 inch per minute
At the end of each minute, the rubber band instantaneously stretches in length by 8 inches
How long if ever will it take for the inchworm to reach the end of the rubber band?
Never
At N=0 when he initially crawled onto the end of it?
Sounds like some of the numbers are off.
A caterpillar crawls onto an infinitely elastic rubber band.
The initial length of the rubber band is 8 inches.
The inchworm moves forward along the rubber band at a rate of 1 inch per minute
At the end of each minute, the rubber band instantaneously stretches in length by 8 inches
How long if ever will it take for the inchworm to reach the end of the rubber band?
End of Minute 1:
Band = 16 inches (8 inch original plus 8 inch stretch)
Earthworm travel = 1 inch
End of Minute 2:
Band = 24 inches
Earthworm travel = 2 inch
End of Minute 3:
Band = 32 inches
Earthworm travel = 3 inch
Or, if you consider the inchworm moved slightly each time the band stretched:
End of Minute 1:
Band = 16 inches (8 inch original plus 8 inch stretch)
Earthworm travel = 1 1/8 inch (1 inch of crawling and 1/8 of position change due to the stretch).
End of Minute 2:
Band = 24 inches
Earthworm travel = 2 1/4 inch
End of Minute 3:
Band = 32 inches
Earthworm travel = 3 3/8 inch
Does the rubber band stretch away from the beginning towards, the end, so that the caterpillar has 17 inches to go after the first minute?
Or does the band stretch behind the caterpillar, so that it is now on inch 8 of a 17 inch band after the first minute?
Does it stretch equally in both directions? Does one direction stretch more than another, even if both directions stretch?